Find the lengths of the legs. (NO LINKS)

Question

asked Jun 27, 2022 230k views

1 Answer

Roman Dobrovenskii · Answer 1 · 2022-07-02T22:23:56+0000

Given:

The figure of a right angle triangle with hypotenuse 10 and two angles
$45^\circ, 90^\circ$

To find:

The lengths of the legs.

Solution:

Two angles are given. By using the angle sum property, the third angle is:

Third angle =
$180^\circ-45^\circ- 90^\circ$

=
$45^\circ$

Base angles are equal it means the given triangle is an isosceles right triangle. So, the lengths of both legs are equal.

Let x be the lengths of both legs. Then by using Pythagoras theorem, we get

Hypotenuse^2=leg_1^2+leg_2^2

(10)^2=x^2+x^2

100=2x^2

(100)/(2)=x^2

50=x^2

Taking square root on both sides, we get

$\pm √(50)=x$

$\pm 5√(2)=x$

The side length cannot be negative. So, the only value of x is
5√(2) .

Therefore, the length of the both legs is
5√(2) units.