Question

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

Answer 1

Answer:

a is 53.8°, and b is 36.2°

Step-by-step explanation:

Using sine trig rule:

${ \boxed{ \bf{ \sin(b) = \frac{opposite}{hypotenuse} }}}$

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

Summation of angles of triangle:

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