Question

Besides the 90degree angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree

Answer 1

b.) 23° and 67°

Explanation:

Besides the 90° angle measure, what are the other two angle measures of a right triangle with side lengths 5, 12, and 13? Round to the nearest degree.

a.) 18° and 39°

b.) 23° and 67°

c.) 43° and 47°

d.) 65° and 25°

Answer 2

The other two angle measures are 23 degrees and 67 degrees

Explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

`m\angle A+m\angle C=90^o` ----> by complementary angles

`sin(C)=(AB)/(AC)` ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

`sin(C)=(5)/(13)`

`C=sin^(-1) ((5)/(13))=23^o`

Find the measure of angle A

`m\angle A+23^o=90^o\\m\angle A=67^o`

therefore

The other two angle measures are 23 degrees and 67 degrees