Question

1. find the value of x, round to the nearest tenth, if necessary.

12
(image of a right triangle with hypotenuse 12 cm, angle 40° at the left vertex, and x as the length of the adjacent side to the 40° angle)

Explanation:

Step1: Identify triangle type and trigonometric ratio

The triangle is a right triangle (implied by the right angle, as it's a triangle with a 40° angle and we can assume the right angle is between the side \( x \) and the vertical side). The hypotenuse is 12 cm, and we need to find the adjacent side to the 40° angle, which is \( x \). We use the cosine function: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
So, \( \cos(40^\circ) = \frac{x}{12} \).

Step2: Solve for \( x \)

Multiply both sides by 12: \( x = 12 \times \cos(40^\circ) \).
Calculate \( \cos(40^\circ) \approx 0.7660 \).
Then \( x \approx 12 \times 0.7660 = 9.192 \).
Round to the nearest tenth: \( x \approx 9.2 \).

Answer:

\( x \approx 9.2 \) cm