Geometry Sin Cos Tan Worksheet Hotsell | www.jegrimpe.com - Free Printable

Let’s solve each problem step by step. We’ll use trigonometry ratios:
- Sine (sin) = opposite / hypotenuse
- Cosine (cos) = adjacent / hypotenuse
- Tangent (tan) = opposite / adjacent

We’ll also use inverse functions (like tan⁻¹, sin⁻¹, cos⁻¹) to find angles when we know the sides.

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Section A: Find the missing angle x

#### 1) Triangle with sides 4 cm (opposite), 9 cm (hypotenuse)
Angle x is at the bottom right → opposite side = 4 cm, hypotenuse = 9 cm
→ Use sin(x) = opposite/hypotenuse = 4/9
→ x = sin⁻¹(4/9) ≈ sin⁻¹(0.4444) ≈ 26.4°

#### 2) Triangle with sides 10 cm (adjacent), 14 cm (hypotenuse)
Angle x is at bottom right → adjacent = 10, hypotenuse = 14
→ cos(x) = 10/14 ≈ 0.7143
→ x = cos⁻¹(0.7143) ≈ 44.4°

#### 3) Triangle with sides 7 cm (opposite), 12 cm (adjacent)
Angle x is at bottom right → opposite = 7, adjacent = 12
→ tan(x) = 7/12 ≈ 0.5833
→ x = tan⁻¹(0.5833) ≈ 30.3°

#### 4) Triangle with sides 15 cm (adjacent), 18 cm (hypotenuse)
Angle x is at top left → adjacent = 15, hypotenuse = 18
→ cos(x) = 15/18 ≈ 0.8333
→ x = cos⁻¹(0.8333) ≈ 33.6°

#### 5) Triangle with sides 0.83 cm (adjacent), 0.99 cm (opposite)
Angle x is at top → opposite = 0.99, adjacent = 0.83
→ tan(x) = 0.99 / 0.83 ≈ 1.1928
→ x = tan⁻¹(1.1928) ≈ 50.0°

#### 6) Triangle with sides 410 mm (opposite), 972 mm (hypotenuse)
Angle x is at top right → opposite = 410, hypotenuse = 972
→ sin(x) = 410 / 972 ≈ 0.4218
→ x = sin⁻¹(0.4218) ≈ 25.0°

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Section B: Find missing angles or lengths x

#### 1) Sides 5 cm (opposite), 11 cm (adjacent) → find angle x
tan(x) = 5/11 ≈ 0.4545
x = tan⁻¹(0.4545) ≈ 24.4°

#### 2) Sides 0.21 cm (adjacent), 0.7 cm (hypotenuse) → find angle x
cos(x) = 0.21 / 0.7 = 0.3
x = cos⁻¹(0.3) ≈ 72.5°

#### 3) Side 6.4 cm (opposite), angle 62° → find adjacent side x
tan(62°) = opposite / adjacent = 6.4 / x
→ x = 6.4 / tan(62°)
tan(62°) ≈ 1.8807
→ x ≈ 6.4 / 1.8807 ≈ 3.40 cm

#### 4) Sides 1.5 cm (adjacent), 27 mm (opposite) → find angle x
First, convert units! 27 mm = 2.7 cm
tan(x) = opposite / adjacent = 2.7 / 1.5 = 1.8
x = tan⁻¹(1.8) ≈ 60.9°

#### 5) Angle 13°, adjacent = 2.3 cm → find opposite side x
tan(13°) = x / 2.3
→ x = 2.3 × tan(13°)
tan(13°) ≈ 0.2309
→ x ≈ 2.3 × 0.2309 ≈ 0.531 cm

#### 6) Sides 620 cm (opposite), 8 m (hypotenuse) → find angle x
Convert units: 8 m = 800 cm
sin(x) = 620 / 800 = 0.775
x = sin⁻¹(0.775) ≈ 50.8°

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Final Answer:

Section A:
1) x = 26.4°
2) x = 44.4°
3) x = 30.3°
4) x = 33.6°
5) x = 50.0°
6) x = 25.0°

Section B:
1) x = 24.4°
2) x = 72.5°
3) x = 3.40 cm
4) x = 60.9°
5) x = 0.531 cm
6) x = 50.8°