Question

A right triangle has a hypotenuse of length 59 and one leg of length 23.

Part A: Determjne the angle measure of the other two acute angles in the triangle. Round to the nearest hundredth.

Part B: Determine the side length of the other leg.

Answer 1

Part A) The measure of the other two acutes angles are
`=67.06\°` and
`22.94\°`

Part B) The side length of the other leg is equal to
`54.33\ units`

Explanation:

Part A)

see the attached figure to better understand the problem

we know that

In the right triangle ABC

`cos(A)=(AB)/(AC)`

substitute the values

`cos(A)=(23)/(59)`

`A=arccos((23)/(59))=67.06\°`

Remember that

`A+C=90\°` -------> by complementary angles

`C=90\°-67.06\°=22.94\°`

Part B)

Applying the Pythagoras Theorem

`CB^(2)=AC^(2)-AB^(2)`

substitute

`CB^(2)=59^(2)-23^(2)`

`CB^(2)=2,952`

`CB=54.33\ units`