Let’s solve each problem step by step. We’ll use inverse trigonometric functions (like sin⁻¹, cos¹, tan⁻¹) on a calculator to find the angle measures. Make sure your calculator is in
degree mode.
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Problem 1: sin A = 0.5150 → Find A
→ Use sin⁻¹(0.5150)
→ sin⁻¹(0.5150) ≈ 31.0°
✔ Rounded to nearest degree:
31°
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Problem 2: cos A = 0.7431 → Find A
→ Use cos⁻¹(0.7431)
→ cos⁻¹(0.7431) ≈ 42.0°
✔ Rounded to nearest degree:
42°
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Problem 3: cos W = 0.6157 → Find W
→ Use cos⁻¹(0.6157)
→ cos⁻¹(0.6157) ≈ 52.0°
✔ Rounded to nearest degree:
52°
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Problem 4: cos A = 0.5878 → Find A
→ Use cos⁻¹(0.5878)
→ cos¹(0.5878) ≈ 54.0°
✔ Rounded to nearest degree:
54°
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Problem 5: tan W = 10.0013 → Find W
→ Use tan⁻¹(10.0013)
→ tan⁻¹(10.0013) ≈ 84.3°
✔ Rounded to nearest degree:
84°
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Problem 6: cos A = 0.4226 → Find A
→ Use cos⁻¹(0.4226)
→ cos⁻¹(0.4226) ≈ 65.0°
✔ Rounded to nearest degree:
65°
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Problem 7: tan W = 0.5317 → Find W
→ Use tan⁻¹(0.5317)
→ tan⁻¹(0.5317) ≈ 28.0°
✔ Rounded to nearest degree:
28°
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Now for the triangle problems — we’re given two sides and need to find an indicated angle using trig ratios.
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Problem 9: Right triangle with opposite = 17, adjacent = 20 → Find angle at bottom left
→ This is tangent: tan(θ) = opposite / adjacent = 17/20 = 0.85
→ θ = tan⁻¹(0.85) ≈ 40.4°
✔ Rounded to nearest degree:
40°
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Problem 10: Right triangle with opposite = 9, hypotenuse = 25 → Find angle at bottom left
→ This is sine: sin(θ) = opposite / hypotenuse = 9/25 = 0.36
→ θ = sin⁻¹(0.36) ≈ 21.1°
✔ Rounded to nearest degree:
21°
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Problem 11: Right triangle with adjacent = 20, hypotenuse = 29 → Find angle at bottom left
→ This is cosine: cos(θ) = adjacent / hypotenuse = 20/29 ≈ 0.6897
→ θ = cos⁻¹(0.6897) ≈ 46.4°
✔ Rounded to nearest degree:
46°
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Problem 12: Right triangle with opposite = 40, adjacent = 44 → Find angle at top (between hypotenuse and vertical side)
Wait — let’s look carefully. The right angle is at the bottom right. The angle marked “x” is at the top vertex. So relative to that angle:
- Opposite side = 44 (horizontal leg)
- Adjacent side = 40 (vertical leg)
So tan(x) = opposite / adjacent = 44/40 = 1.1
→ x = tan⁻¹(1.1) ≈ 47.7°
✔ Rounded to nearest degree:
48°
*(Note: If you thought it was the other angle, double-check which angle is labeled. Based on standard labeling, if x is at the top, then yes — opposite is horizontal side.)*
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Problem 13: Right triangle with opposite = 12, hypotenuse = 30 → Find angle at bottom left
→ sin(θ) = 12/30 = 0.4
→ θ = sin⁻¹(0.4) ≈ 23.6°
✔ Rounded to nearest degree:
24°
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Problem 14: Right triangle with adjacent = 17, hypotenuse = 37 → Find angle at bottom left
→ cos(θ) = 17/37 ≈ 0.4595
→ θ = cos⁻¹(0.4595) ≈ 62.6°
✔ Rounded to nearest degree:
63°
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Final Answer:
1) 31°
2) 42°
3) 52°
4) 54°
5) 84°
6) 65°
7) 28°
9) 40°
10) 21°
11) 46°
12) 48°
13) 24°
14) 63°
Parent Tip: Review the logic above to help your child master the concept of trigonometry worksheet kuta.
