Question

Solve for r in the triangle. Round your answer to the nearest tenth.

Answer 1

Based on the right-angled triangle shown above, the value of x is equal to 6.9 units.

In order to determine the value of x, we would have to apply the basic cosine trigonometric function because the given side lengths represent the adjacent side (x) and hypotenuse (12) of a right-angled triangle;

cos(θ) = Adj/Hyp

Where:

• Adj represent the adjacent side of a right-angled triangle.
• Hyp represent the hypotenuse of a right-angled triangle.
• θ represent the angle.

By applying the cosine trigonometric function ratio to right-angled triangle ABC, we have the following:

cos(θ) = adjacent side/hypotenuse

cos(90 - 35) = x/12

cos(55) = x/12

x = 12cos(55)

x = 6.8829 ≈ 6.9 units.

Answer 2

6.9 =x

Explanation:

Since this is a right triangle, we can use trig functions

sin theta = opp/hyp

sin 35 = x/12

12 sin 35 = x

6.882917236 = x

To the nearest tenth

6.9 =x