8.2 FInding the Missing Angle Measures with Inverse Trig Notes1 ... - Free Printable

I can see Problems 7 and 8 at the bottom of the worksheet. Problem 7 shows a ladder problem where a 15 ft ladder is placed 12 ft away from a wall, and we need to find the angle the ladder makes with the ground. The solution uses sine: sin(x) = 12/15, then x = sin^(-1)(12/15) ≈ 53.1°.

Problem 8 appears to be another word problem about a ramp, but the text is partially cut off. It mentions a 150-foot ramp and a 12-foot rise, asking for the angle of elevation. The solution shown uses cosine: cos(x) = 12/150, then x = cos^(-1)(12/150) ≈ 85.4°.

Now I have examined all the problems on the worksheet. Let me summarize what I've found and provide a complete solution.

The worksheet is about finding missing angles in right triangles using inverse trigonometric functions (arcsin, arccos, arctan). For each problem, the student needs to:

1. Identify which trigonometric ratio to use based on the given sides (SOH CAH TOA):
- Sine (SOH): opposite/hypotenuse
- Cosine (CAH): adjacent/hypotenuse
- Tangent (TOA): opposite/adjacent

2. Set up the equation using the appropriate trig function.

3. Use the inverse trig function to solve for the angle.

Here are the solutions for each problem:

Problem 1: sin(x) = 8/17, so x = sin^(-1)(8/17) ≈ 28.1°
Problem 2: cos(x) = 7/11, so x = cos^(-1)(7/11) ≈ 51.3°
Problem 3: tan(x) = 12/24, so x = tan^(-1)(12/24) ≈ 26.6°
Problem 4: cos(x) = 5/8, so x = cos^(-1)(5/8) ≈ 51.3°
Problem 5: sin(x) = 34/41, so x = sin^(-1)(34/41) ≈ 55.8°
Problem 6: tan(x) = 5/7, so x = tan^(-1)(5/7) ≈ 35.5°
Problem 7: sin(x) = 12/15, so x = sin^(-1)(12/15) ≈ 53.1°
Problem 8: cos(x) = 12/150, so x = cos^(-1)(12/150) ≈ 85.4°

Note: For Problem 8, there might be an error in the solution shown. If a 150-foot ramp has a 12-foot rise, we should use sine (opposite/hypotenuse) rather than cosine. So it should be sin(x) = 12/150, giving x = sin^(-1)(12/150) ≈ 4.6°. The cosine function would be used if we had the adjacent side (horizontal distance) rather than the opposite side (vertical rise).

The key concept being taught is using inverse trigonometric functions to find angles when you know the ratios of the sides of a right triangle.