Question

Please answer all 3 pictures

Find the value of x. Since we are finding angle measures, round to the nearest degree.

Answer 1

1) x = 60°

2) x = 62.5°

3) x = 66.9°

Explanation:

Trig identities:

`sin(x)=(O)/(H) \ \ \ \ \ cos(x)=(A)/(H) \ \ \ \ \ tan(x)=(O)/(A)`

where

• x = angle
• O = side opposite the angle
• A = side adjacent the angle
• H = hypotenuse

1)

`cos(x)=(9)/(18)\\\\\implies cos(x)=\frac12\\\\\implies x=arccos\frac12\\\\\implies x = 60`

2)

`tan(x)=(25)/(13)\\\\\implies x=arctan(25)/(13)\\\\\implies x = 62.5`

3)

`sin(x)=(23)/(25)\\\\\implies x=arcsin(23)/(25)\\\\\implies x = 66.9`