Question

Find θ in the triangle. Round to the nearest degree.

a.
30º
b.
27º
c.
21º
d.
34º

Answer 1

cosine theta = adj / hypotenuse

cosine theta = 72 / 87

cosine theta = 0.8275862069

arc cosine (0.8275862069) = 24.148 degrees

answer is d

Answer 2

d. 34°

Explanation:

In the question above, we are ask to find Ф, to find Ф we can simply use trigonometric formula and they are;

SOH CAH TOA

sin Ф = opposite / hypotenuse

cos Ф = adjacent / hypotenuse

tan Ф = opposite / adjacent

The side considered adjacent is that side that both the angle Ф and angle the right angle is formed. The hypotenuse side is the side opposite to the right angle.

So from the diagram above, adjacent = 72 and hypotenuse =87, since we were giving just adjacent and opposite, the best trig. formula to use is CAH.

So lets proceed;

cos Ф = adjacent / hypotenuse

= 72 / 87

= 0.82759

cos Ф = 0.82759

To get the value of Ф , we simply take the
`cos^(-1)` of Ф

so;

cos Ф = 0.82759

Ф =
`cos^(-1)` ( 0.82759)

Ф = 34.1

Ф = 34° to the nearest degree