Question

What is the value of x? Round to the nearest hundredth.

Answer 1

Explanation:

You need to use trigonometry (SOHCAHTOA)

As from the focus angle -thetre- (65^o) you have the adjecent (x) and hypotenuse (the side opposite the right angle - 81.9m):

cos(θ) = adjacent/hypotenuse

cos (65) = x/81.9

as the opposite of dividing is mulitplying, you multiple both sides by 81.9

81.9*cos(65) = x

using calculator - in degree mode-

x = 34.6124

Thus it is the first choice, x = 34.61.

Answer 2

The correct answer is first option

X = 34.61

Explanation:

Points to remember

Trigonometric ratios

Sin θ = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

From the figure we can see that a right angled triangle with base x and hypotenuse = 81.9.

One angle = 65°

To find the value of x

We have Cos θ = Adjacent side/Hypotenuse

Cos 65 = X/81.9

X = 81.9 * Cos 65

= 81.9 * 0.4226

= 34.61

Therefore X = 34.61

The correct answer is first option