Question

Use a trigonometric ratio to find the value of x. round your answer to nearest tenth

Answer 1

Here the angle is given as 55°

With respect to 55°,

8.9 cm is the opposite side

x cm is the adjacent side.

The trigonometric ratio associating these sides is tan

$tan\theta=\frac{Opposite}{Adjacent}$

Substituting the values we get

$\frac{8.9}{x}=tan55^{o}$

Multiplying both sides by x we get

$8.9=xtan55^{o}$

Dividing by tan55° on both sides

$\frac{8.9}{tan55^{o} } =x$

So we get

$x=6.2$ cm

Option a) is the right answer.

Answer 2

The trigonometry ratio that we shall use to solve the question will be:
tan θ=opposite/adjacent
where:
opposite=8.9 cm
adjacent =x cm
θ=55°
plugging the values and simplifying we obtain:
tan 55=8.9/x
thus
x=8.9/tan55
x=6.23 cm~6.2 cm
Answer: A