Question

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

a. 6.2 cm
b. 12.7 cm
c. 15.5 cm
d. 10.9 cm

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=(Opposite)/(Adjacent)`

Substituting the values we get

`(8.9)/(x)=tan55^(o)`

Multiplying both sides by x we get

`8.9=xtan55^(o)`

Dividing by tan55° on both sides

`(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