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

Answer:

b.) 23° and 67°

Step-by-step 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

Answer:

The other two angle measures are 23 degrees and 67 degrees

Step-by-step 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

$sin(C)=\frac{AB}{AC}$ ----> by SOH (opposite side divided by the hypotenuse)

substitute the given values

$sin(C)=\frac{5}{13}$

$C=sin^{-1} (\frac{5}{13})=23^o$

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