Question

Using the Pythagorean theorem, how do you find the length of a leg of a right angled triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long.

Answer 1

Hint: We will first take one feet as the base and the other feet as the perpendicular of the triangle. Since, we already have the hypotenuse, so putting all the known values in $P^2+B^2=H^2$ to get the required value.

Complete step by step solution:
We are given that we are required to find the length of a leg of a right angled triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long using the Pythagorean Theorem.
Let us assume that the given leg which is 8 feet long be the base of the right angled triangle given to us. Now, let us also assume that the other leg that we are required to find is the length of the perpendicular of the right angled triangle given to us.
Putting the values: H = 10 feet and B = 8 feet in the Pythagorean formula $P^2+B^2=H^2$, we will then obtain the following equation with us:-
$\Rightarrow P^2+8^2={10}^2$
Opening up the square and simplifying, we will then obtain the following equation:-
$\Rightarrow P^2+64=100$
Taking 64 from addition in the left hand side to subtraction in the right hand side, we will then obtain the following equation with us:-
$\Rightarrow P^2=100-64$
Simplifying the calculations on the right hand side, we will then obtain the following expression:-
$\Rightarrow P^2=36$
Taking square – root on both the sides of above equation, we will then obtain the following equation:-
$\Rightarrow P=6$

Hence, the length of the leg is 6 feet.

Note:-
The students must note that the Pythagorean Theorem which we used in the above solution states that: In a right angled triangle, the following expression always satisfies:-
$\Rightarrow P^2+B^2=H^2$
The students must also note that when we took the square – root of both the sides in the last few steps, we got the possibility of P being both 6 and – 6 but since the length of anything can never be negative, so we stuck with P being 6 feet.