Question

Determine the unknown angle measures, to the nearest degree, in the diagram provided.

Answer 1

a is 53.8°, and b is 36.2°

Explanation:

Using sine trig rule:

`{ \boxed{ \bf{ \sin(b) = (opposite)/(hypotenuse) }}}`

`{ \tt{ \sin(b) = (78)/(132) }} \\ \\ { \tt{b = { \sin }^( - 1)( (78)/(132) ) }} \\ \\ { \tt{b = 36.2 \degree}}`

Summation of angles of triangle:

`{ \tt{a + b + 90 \degree = 180 \degree}} \\ { \tt{a + 36.2 \degree + 90 \degree = 180 \degree}} \\ { \tt{a = (180 - 36.2 - 90) \degree}} \\ { \tt{a = 53.8 \degree}}`