Question

Find the lengths of the legs.
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Answer 1

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

$Hypotenuse^2=leg_1^2+leg_2^2$

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

$100=2x^2$

$\dfrac{100}{2}=x^2$

$50=x^2$

Taking square root on both sides, we get

$\pm \sqrt{50}=x$

$\pm 5\sqrt{2}=x$

$\pm 5\sqrt{2}=x$

The side length cannot be negative. So, the only value of x is $5\sqrt{2}$.

Therefore, the length of the both legs is $5\sqrt{2}$ units.