Can the hypotenuse ever be shorter?
Answer and Explanation:
The hypotenuse is always longer than the legs of a right triangle because the legs always meet at a 90-degree angle in a right-angled triangle. Therefore, the hypotenuse that joins the legs' tips must be long enough to enclose the triangle.
Is the hypotenuse always 90?
The hypotenuse side of a right triangle is always across from the 90 degree angle (the little box). It is always the longest side of the triangle. The opposite and adjacent sides of a right triangle are the legs of the triangle and they form the 90 degree angle.
What is not a hypotenuse?
In mathematics, a nonhypotenuse number is a natural number whose square cannot be written as the sum of two nonzero squares. The name stems from the fact that an edge of length equal to a nonhypotenuse number cannot form the hypotenuse of a right angle triangle with integer sides.
Is a always the hypotenuse?
The longest side of the right triangle (the side opposite the 90o angle) is called the hypotenuse and the other two (shorter) sides are called the legs of the triangle. The legs of a right triangle are commonly labeled "a" and "b," while the hypotenuse is labeled "c."
Can the hypotenuse be negative?
The length of the hypotenuse is a number and length is always positive. The coordinates of the vertices of a triangle, in a given coordinate system may be positive or negative but the lengths of the legs of the right triangle are also positive.
How long must the hypotenuse be?
The length of the hypotenuse is equal to Sqrt(a^2+b^2) where a and b are the lengths of the two other sides of the triangle.
What is the angle of depression?
In trigonometry, the angle of depression is the angle formed between the horizontal line and the line of sight when we look downwards at an object. In this angle, the object at which we look is always placed below the horizontal axis or line.
Can hypotenuse be smaller than opposite?
No, the hypotenuse is always longer than the other two sides. How do I find the length of the hypotenuse? You can find the length of the hypotenuse by applying the Pythagorean theorem, which states that the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.
Is Tan the hypotenuse?
The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and given the symbol cos. Finally, the ratio of the opposite side to the adjacent side is called the tangent and given the symbol tan.
Can the hypotenuse be equal?
The answer is simply NO. If the hypotenuse was equal to another side, then you will not have a right-angled triangle.
How do you find sin?
Correct answer:
The ladder, when leaned against the wall, forms a right triangle where the ladder is the hypotenuse, the wall is one leg, and the ground between the ladder and the wall is the other leg.
Is ladder a hypotenuse?
It is not possible to solve a right triangle when only given the hypotenuse. We would need some other piece of information about the triangle in order to solve it. The reason for this has to do with the number of right triangles that we can create with a given hypotenuse.
What if I only know the hypotenuse?
The 30-60-90 triangle rule is for finding the the lengths of two sides when one side is given. The shorter side is opposite the 30 degree angle, the longer side is opposite the 60 degree angle, and the hypotenuse is opposite the 90 degree angle.
What is the 30 60 90 triangle rule?
Pythagorean triples are a2+b2 = c2 where a, b and c are the three positive integers. These triples are represented as (a,b,c). Here, a is the perpendicular, b is the base and c is the hypotenuse of the right-angled triangle. The most known and smallest triplets are (3,4,5).
What is the smallest Pythagorean triple?
How to Find the Value of Cos 90 Degrees? The value of cos 90 degrees can be calculated by constructing an angle of 90° with the x-axis, and then finding the coordinates of the corresponding point (0, 1) on the unit circle. The value of cos 90° is equal to the x-coordinate (0). ∴ cos 90° = 0.
Why is cos 90 zero?
The side opposite the right angle is called the hypotenuse. We label the side opposite θ as the opposite and the remaining side as the adjacent. Using these names we can list the following standard ratios: sinθ=oppositehypotenuse,cosθ=adjacenthypotenuse,tanθ=oppositeadjacent.
Can the hypotenuse also be the opposite?
side lengths of triangles cannot be negative, so we can disregard this inequality.
Can a triangle be negative?
Therefore, AC is the largest side in ∆ABC. However, AC is the hypotenuse of ∆ABC. Therefore, the hypotenuse is the longest side in a right-angled triangle.
What is the longest hypotenuse?
It is a right triangle if one of the three angles is a right angle. The Pythagorean theorem implies the theorem that the hypotenuse is greater than either leg of a right triangle. There is no right triangle in which the hypotenuse is equal to a leg.
Can the hypotenuse be equal to a leg?
The exact value of sin 30 degrees is ½.
How to find hypotenuse?
The angle of elevation is the angle formed between the horizontal and our line of sight when we look up. The angle of depression equals the angle of elevation because they from alternate interior angles or congruent angles located on different parallel lines cut by a transversal line.
What is the value of sin 30?
Technically, yes, angle can be represented as a vector in certain mathematical applications. However, in most cases, angle is considered to be a scalar quantity.
Is angle of depression equal?
Why is sin opposite over hypotenuse? Because we choose to call the relationship in a right triangle between an acute angle and the ratio of its opposite leg to the hypotenuse a sine. The sine function takes an angle measure, in degrees or radians, and converts it to the ratio opposite/hypotenuse.
Is An angle A vector?
To find the longest side we use the hypotenuse theorem, (Hypotenuse)2 = (Base)2 + (Altitude)2. For example, a bread slice is given in the shape of a right-angled triangle. If the base is 4 inches and the height is 3 inches, then the hypotenuse is (H)2 = (4)2 + (3)2 = √{16+9} = √25 = 5 inches.
Why is sin opposite over hypotenuse?
No, it can't. The largest angle in a right triangle is 90 degrees and it is the largest angle of the triangle. The side opposite the largest angle has to be the largest side.
What is an example of a hypotenuse?
Sin and Cos are basic trigonometric functions along with tan function, in trigonometry. The sine of an angle is equal to the ratio of the opposite side to the hypotenuse whereas the cosine of an angle is equal to the ratio of the adjacent side to the hypotenuse.
Can the opposite be larger than the hypotenuse?
This makes Hipparchus the founder of trigonometry. The next Greek mathematician to produce a table of chords was Menelaus in about 100 AD. Menelaus worked in Rome producing six books of tables of chords which have been lost but his work on spherics has survived and is the earliest known work on spherical trigonometry.
What does sin equal?
The ratio of the opposite side and the hypotenuse is known as sine theta. Consider the below right-angled triangle ABC, Sin θ = opposite side/hypotenuse = CB/AC.
Who invented trigonometry?
For a set of triangles to be congruent, their respective sides and angles should be equal. In case of a triangle with all respective angles equal i.e. AAA condition, the sides of the triangles may or may not be equal.
What is sin theta?
Why do we call the Pythagorean Theorem a theorem, not a law? As far as I know, we call a theorem a theorem because though it's reliable in every observable case, its truthfulness cannot be proven for every case.
Is AAA congruent?
To get a perfectly square corner, you want to aim for a measurement ratio of 3:4:5. In other words, you want a three-foot length on your straight line, a four-foot length on your perpendicular line, and a five-foot length across. If all three measurements are correct, you'll have a perfectly square corner.
Why is Pythagorean theorem not a law?
The value of sin 0° is 0.
What is the 3 4 5 rule for square?
The angle, whose sine is 1, is the inverse function of sin 1. As sine of the angle 90° is 1, it is equal to the function sin 1. So, the inverse function of sin 1 is denoted as 90° or π/2.
What is the sin at 0?
In trigonometry, arctan is the inverse of the tangent function and is used to compute the angle measure from the tangent ratio (tan = opposite/adjacent) of a right triangle. Arctan can be calculated in terms of degrees and as well as radians. ( x ) = 2 arctan
Where does sin equal to 1?
In a right triangle, the hypotenuse is the longest side, an "opposite" side is the one across from a given angle, and an "adjacent" side is next to a given angle. We use special words to describe the sides of right triangles. The hypotenuse of a right triangle is always the side opposite the right angle.
What is arctan in math?
The hypotenuse side of a right triangle is always across from the 90 degree angle (the little box). It is always the longest side of the triangle. The opposite and adjacent sides of a right triangle are the legs of the triangle and they form the 90 degree angle.
Is hypotenuse shortest?
In geometry, a hypotenuse is the longest side of a right triangle. It's also the side opposite the right angle. The word hypotenuse means 'length under' or 'stretch under.
Is the hypotenuse always 90?
-Remember that because the radius of the circle is 1, the hypotenuse of each triangle is always 1 within the unit circle.
Why is a hypotenuse?
The length of the hypotenuse is a number and length is always positive. The coordinates of the vertices of a triangle, in a given coordinate system may be positive or negative but the lengths of the legs of the right triangle are also positive.
Is the hypotenuse always 1?
In a right triangle, the longest side of the triangle is called the hypotenuse. The hypotenuse is always the side opposite the right angle. The other two sides of a right triangle are called the legs of the triangle.
Can the hypotenuse ever be negative?
A 45-45-90 triangle is a special type of right triangle, where the ratio of the lengths of the sides of a 45-45-90 triangle is always 1:1:√2, meaning that if one leg is x units long, then the other leg is also x units long, and the hypotenuse is x√2 units long.
Is the hypotenuse always a?
There are 2π radians in a full circle. (So 2π radians should equal 360°. Check it out by multiplying 57.30° by 2π = 6.283. You should get 360° to four significant figures.)
What is the 45-45-90 rule?
No. The sides of a 30–60–90 triangle are in the proportion 1 - √3 - 2, not 3–4–5. Or, looking at it the other way, the angles of a 3–4–5 triangle are about 36.87°, 53.13° and 90°.
How many radians is a circle?
∴ Pythagorean triplet = 20, 99, 101.
Is a 345 Triangle a 30 60 90?
Plug the given numbers into the Pythagorean Theorem. Yes, 9, 40, 41 is a Pythagorean Triple and sides of a right triangle.
Is 20 99 and 101 a Pythagorean triplet?
3,4,5 is a Pythagorean triplet.
Is 9 40 41 a right triangle?
The value of cos 0 is 1. Here, we will discuss the value for cos 0 degrees and how the values are derived using the quadrants of a unit circle. The trigonometric functions are also known as an angle function that relates the angles of a triangle to the length of the triangle sides.
Is 346 a Pythagorean triplet?
cos(0) = 1
The lengths of the hypotenuse and side adjacent to the angle increase closer and closer as the angle gets smaller. The hypotenuse and adjacent side will fit perfectly on top of each other once the angle measurement reaches zero, forming a 1-to-1 ratio. As a result, the cosine of 0 equals 1.
Can cosine be 0?
The 30-60-90 triangle rule is for finding the the lengths of two sides when one side is given. The shorter side is opposite the 30 degree angle, the longer side is opposite the 60 degree angle, and the hypotenuse is opposite the 90 degree angle.
What happens when cosine is 0?
If the angles are smaller, so must be their opposite sides. So the hypotenuse is always longer than either leg.
What is the 30 60 90 triangle rule?
As length represents a distance between two points that cannot be negative.
Can the hypotenuse be smaller than the opposite?
In the third quadrant, all x and y values will be negative, so all sine and cosine values will be negative.
Can side lengths be negative?
The hypotenuse theorem is defined by Pythagoras theorem, According to this theorem, the square of the hypotenuse side of a right-angled triangle is equal to the sum of squares of base and perpendicular of the same triangle, such that; Hypotenuse2 = Base2 + Perpendicular2.
Can sine be negative?
Can a leg be bigger than the hypotenuse?
Why is hypotenuse 1?
What is opposite leg hypotenuse?
What is the hypotenuse rule?
No, the hypotenuse is always longer than the other two sides.
Can the hypotenuse be shorter than the other sides?
If the angles are smaller, so must be their opposite sides. So the hypotenuse is always longer than either leg.
Can the hypotenuse be smaller than the opposite?
In any right triangle, the hypotenuse is greater than any one of the other sides, but less than their sum because to form a triangle sum of any two sides must be greater than the third side.
Will a triangle's hypotenuse ever be smaller than its sides?
A hypotenuse is always longer than each of the other two sides, and always shorter than the total length of the other two sides.