Question

using trigonometry to find lengths
find the missing side. round to the nearest tenth.
1)
2)
3)
4)
5)
6)
7)
8)

Explanation:

Let's solve problem 1 first (assuming the triangle in problem 1 is a right triangle with angle 35°, adjacent side 14, and opposite side \( x \)):

Step 1: Identify trigonometric ratio

We have a right triangle, angle \( 35^\circ \), adjacent side \( 14 \), opposite side \( x \). So we use tangent: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)
\( \tan(35^\circ) = \frac{x}{14} \)

Step 2: Solve for \( x \)

Multiply both sides by 14: \( x = 14 \times \tan(35^\circ) \)
Calculate \( \tan(35^\circ) \approx 0.7002 \)
\( x \approx 14 \times 0.7002 \approx 9.8 \)

Answer:

For problem 1, the missing side \( x \approx 9.8 \) (rounded to the nearest tenth).

(If you want solutions for other problems, please clarify the details of each triangle, like which angle, which sides are given, etc.)