Chapter J.28, Problem 1E

Find the length of the third side of each right triangle. Where appropriate give both an exact answer and an approximation to three decimal places.

1.

To determine

The length of the third side of the given right triangle.

Answer to Problem 1E

The length of the third side of the given right triangle is 17.

Explanation of Solution

Theorem used:

In any right triangle, if a and b are the legs and c is the length of the hypotenuse, then the Pythagorean equation is $a^2+b^2=c^2$.

Calculation:

From the given figure, it is clear that the length of the legs are 15 and 8.

Use Pythagorean Theorem and obtain the length of the side c as follows.

$\begin{array}{l}{a}^2+b^2=c^2\\ 8^2+{15}^2=c^2\\ 64+225=c^2\end{array}$

On further simplifications,

$\begin{array}{l}289=c^2\\ \sqrt{289}=c\left(\text{Taking square root on both sides}\right)\\ 17=c\end{array}$

Therefore, the length of the third side of the given right triangle is 17.