Question

Given a 45-45-90 triangle with the hypotenuse measuring 5√7 feet. Which is the exact measure of each leg?

Answer 1

Answer:

Step-by-step explanation:

First, we know a 45-45-90 triangle has two legs that are the same because two angles are the same, so we can say that:

$a^2+b^2=c^2=a^2+a^2=c^2$

Remember that $a^2$ and $a^2$ are the legs, which are the same length, so we can do this. Now, we solve the equation.

$a^2+a^2=c^2\\2a^2=5\sqrt{7}\\2a=(5\sqrt{7})^2\\2a=5\\a=\frac{5}{2}$

HOPE THIS HELPS :D

Answer 2

The Pythagoras is the sum of the square of two sides equal to the square of the longest side. Then the exact measure of each leg is 9.4 ft.

What is a right-angle triangle?

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

A right-angle 45-45-90 triangle with the hypotenuse measuring 5√7 feet.

We know that if two angles of any triangle are the same then their opposite sides are also the same.

Let each side length of x ft. Then by the Pythagoras theorem. we have

$\begin{aligned} x^2 + x^2 &= (5\sqrt7)^2\\\\2x^2 &= 25 \times 7\\\\x^2 &= \dfrac{175}{2}\\\\x^2 &= 87.5\\\\x &= 9.354 \approx 9.4 \ \rm ft \end{aligned}$

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177