Question

In a right triangle with legs 5 cm and 12 cm long, find the measure of the smallest angle

Answer 1

The smallest angle would be opposite the 5 cm side
tan (angle) = 5 / 12
tan (angle) = 0.4166666667
arc tan ( 0.4166666667 ) = 22.62 degrees

Answer 2

The measure of the smallest angle is
`22.6\°`

Explanation:

see the attached figure to better understand the problem

we know that

In the right triangle ABC

`tan(A)=(BC)/(AB)`

substitute

`tan(A)=(12)/(5)`

`A=tan^(-1)((12)/(5))= 67.4\°`

Find the measure of angle C

Remember that

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

`m<C=90\°-67.4\°=22.6\°`