Question

unit 8: right triangles & trigonometry
homework 4: trigonometry ratios & finding missing sides
this is a 2 - page document!
directions: give each trig ratio as a fraction in simplest form.
1)

• $sin q =$
• $sin r =$
• $cos q =$
• $cos r =$
• $\tan q =$
• $\tan r =$

directions: solve for $x$. round to the nearest tenth.
2)
3)
4)
5)
6)
7)
8)
9)
© gina wilson (all things alg

Explanation:

Let's solve problem 2 (the right triangle with angle \(40^\circ\), leg \(17\), and we need to find \(x\) (the other leg)) as an example.

Step 1: Identify the trigonometric ratio

We have a right triangle, angle \(40^\circ\), adjacent side to the angle is \(17\), and the opposite side is \(x\). So we use the tangent function: \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)
\(\tan(40^\circ)=\frac{x}{17}\)

Step 2: Solve for \(x\)

Multiply both sides by \(17\): \(x = 17\times\tan(40^\circ)\)
We know that \(\tan(40^\circ)\approx0.8391\)
So \(x\approx17\times0.8391\approx14.3\)

Answer:

\(x\approx14.3\) (for problem 2)

If you want solutions for other problems, please specify which one (e.g., problem 3, 4, etc.), and we can follow a similar process using sine, cosine, or tangent depending on the given sides and angles.