Question

Find the value of x to the nearest tenth.
26.2
26.3
80.8
1,530

Answer 1

x = 26.3

Explanation:

There are three trigonometric rules that this question will apply to, they are:

`Sin\theta(opp)/(hyp) Cos\theta(adj)/(hyp) Tan\theta(opp)/(adj)`

Where opp is the length of the side opposite to angle Φ, hyp is the hypotenuse of the triangle and adj is the length of a side adjacent to angle Φ.

In the provided picture, angle Φ has been provided alongside the hypotenuse with the opposite side length needing to be calculated. A trig function that includes all three of these must be used. The only one that does have all three is sin, ergo it is what we will use.

In the current equation form, the subject is incorrect and need to be changed so that it becomes the opposite side.

`Sin\theta = (opp)/(hyp)\\ opp = sin\theta \cdot hyp`

Plug the known values in:

`x = Sin(18\textdegree) \cdot 85\\x = 0.3090169 \cdot 85\\x = 26.266\\x = 26.3`

Hope this helps!