Is a hypotenuse always in a right triangle?
The hypotenuse of a right triangle is always the side opposite the right angle. It is the longest side in a right triangle. The other two sides are called the opposite and adjacent sides. The opposite side is across from a given angle.
Why does the hypotenuse of a right triangle always have to be longer than either leg?
In a right triangle, the sum of the interior angles will always be 180°. Since a right angle is half that (90°), it has to be the biggest angle in the triangle and the side across from it will always be the longest.
Is it possible for the hypotenuse of a right triangle to be equal or smaller than the larger leg in a right triangle?
For every right triangle, the hypotenuse is the diameter of the circumscribed circle: But the diameter is the largest of all possible chords, so it can’t be smaller than any of them. The definition of the hypotenuse is the side opposite of the right angle (90-degrees angle).
What ratio would you use to find an angle if you know the opposite and adjacent sides?
Using these names we can list the following standard ratios: sinθ=oppositehypotenuse,cosθ=adjacenthypotenuse,tanθ=oppositeadjacent. Allied to these are the three reciprocal ratios, cosecant, secant and cotangent: cosecθ=hypotenuseopposite,secθ=hypotenuseadjacent,cotθ=adjacentopposite.
Is hypotenuse always the longest side?
The hypotenuse is always the longest side in a right triangle because it is opposite of the largest angle, the ninety degree angle.
Why is the hypotenuse the longest?
The largest angle in a right triangle is the right angle, therefore, opposite to it lies the longest side – hypotenuse.
Why hypotenuse is the longest side?
Does the hypotenuse have to be the longest side?
The angles in any triangle add up to 180°. In any triangle, the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Thus, in a right triangle, the hypotenuse is always the longest side.
How do I find the hypotenuse of a right triangle?
Hypotenuse calculator The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c , Pythagoras’ theorem states that: a² + b² = c² . To solve for c , take the square root of both sides to get c = √(b²+a²) .