11th grade trigonometry

Example

In triangle ABC, angle A = 44°, angle B = 73° and side a = 14 cm. Find side b to 1 decimal place.

1. b = 14 × sin 73° / sin 44°
2. ≈ 19.3 cm

Answer: 19.3

Example

In triangle ABC, b = 16 cm, c = 9 cm and angle A = 38°. Find side a to 1 decimal place.

1. a² = 256 + 81 − 2 × 16 × 9 × cos 38°
2. a² ≈ 110.053
3. a ≈ 10.5 cm

Answer: 10.5

Example

Two sides of a triangle are 18 cm and 10 cm with an angle of 149° between them. Find the area to 1 decimal place.

1. ½ × 18 × 10 × sin 149° ≈ 46.4 cm²

Answer: 46.4

Example

Convert π/6 radians to degrees.

1. π/6 = 30°

Answer: 30

Example

In triangle ABC, A = 47°, B = 46° and a = 17 cm. Find b to 1 decimal place.

1. b = 17 × sin 46° ÷ sin 47°
2. b ≈ 16.7 cm

Answer: 16.7

Example

In triangle ABC, A = 63°, a = 14 cm and b = 9 cm. Find angle B to 1 decimal place.

1. sin B = 9 × sin 63° ÷ 14 ≈ 0.5728
2. B ≈ 34.9°

Answer: 34.9

Example

In triangle ABC, b = 17 cm, c = 5 cm and A = 82°. Find a to 1 decimal place.

1. a² = 289 + 25 − 2 × 17 × 5 × cos 82° ≈ 290.34
2. a ≈ 17 cm

Answer: 17

Example

A triangle has sides a = 9, b = 10 and c = 6 cm. Find angle A (opposite a) to 1 decimal place.

1. cos A = (100 + 36 − 81)/120 ≈ 0.4583
2. A ≈ 62.7°

Answer: 62.7

Example

You know two sides and an angle opposite one of them; find another angle. Which is the most direct method?

1. Sine rule

Answer: Sine rule

Example

A triangle has area 14.1 cm², one side of 8 cm and an included angle of 118°. Find the other side next to that angle, to the nearest cm.

1. b = 2 × 14.1 ÷ (8 × sin 118°) ≈ 3.99
2. ≈ 4 cm

Answer: 4

Example

Write 180° in radians, as a multiple of π.

1. 180 × π/180 = π

Answer: π

Example

A sector has radius 10 cm and angle 1.2 radians. Find its area.

1. ½ × 10² × 1.2 = 60 cm²

Answer: 60

Example

What are the coordinates of the point on the unit circle at an angle of 225°?

1. (cos 225°, sin 225°) = (−√2/2, −√2/2)

Answer: (−√2/2, −√2/2)

Example

Without a calculator, is sin 108° positive or negative?

1. 108° is in quadrant 2.
2. Positive

Answer: Positive

Example

What is the reference angle for 320°?

1. 360° − 320° = 40°

Answer: 40

Example

A boat sails 45 km on a bearing of 043°. How far east of its start is it? Give 1 decimal place.

1. 45 × sin 43° ≈ 30.7 km

Answer: 30.7