Trigonometry worksheet for solving right triangle problems.

I'll solve each right triangle problem step by step, using trigonometric ratios (sine, cosine, tangent).

Problem 1: Find u
- Given: hypotenuse = 30, angle = 24°, need to find adjacent side u
- Use cosine: cos(24°) = adjacent/hypotenuse = u/30
- u = 30 × cos(24°)
- u = 30 × 0.9135
- u ≈ 27.4

Problem 2: Find z
- Given: adjacent = 52, angle = 27°, need to find opposite side z
- Use tangent: tan(27°) = opposite/adjacent = z/52
- z = 52 × tan(27°)
- z = 52 × 0.5095
- z ≈ 26.5

Problem 3: Find t
- Given: adjacent = 19, angle = 41°, need to find opposite side t
- Use tangent: tan(41°) = opposite/adjacent = t/19
- t = 19 × tan(41°)
- t = 19 × 0.8693
- t ≈ 16.5

Problem 4: Find k
- Given: hypotenuse = 37, angle = 59°, need to find adjacent side k
- Use cosine: cos(59°) = adjacent/hypotenuse = k/37
- k = 37 × cos(59°)
- k = 37 × 0.5150
- k ≈ 19.1

Problem 5: Find r
- Given: opposite = 21, angle = 38°, need to find hypotenuse r
- Use sine: sin(38°) = opposite/hypotenuse = 21/r
- r = 21/sin(38°)
- r = 21/0.6157
- r ≈ 34.1

Problem 6: Find m
- Given: adjacent = 12, angle = 55°, need to find hypotenuse m
- Use cosine: cos(55°) = adjacent/hypotenuse = 12/m
- m = 12/cos(55°)
- m = 12/0.5736
- m ≈ 20.9

Final Answer:
1) u = 27.4
2) z = 26.5
3) t = 16.5
4) k = 19.1
5) r = 34.1
6) m = 20.9