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Trigonometry

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Sample Questions & Solutions

Tangent

cosine

sine

adjacent

Right Angle

Ө

- Given a = 3.25m & b = 3.45m calculate the length of c
- a² + b² = c²
- 3.25² + 3.45² = c²
- 10.5635 + 11.9025 = c²
- 22.466 = c²
- c = √22.466
- c = 4.74m Answer

c

a

b

Question

(c)

(b)

(a)

A

A

(e)

A

A

(f)

(d)

A

A

Copy each of the triangles below and label each of the sides and the angle.

Answer

(c)

(b)

(a)

A

A

(e)

A

A

(f)

(d)

A

A

Copy each of the triangles below and label each of the sides and the angle.

adj

hyp

opp

opp

hyp

opp

hyp

adj

adj

adj

adj

opp

hyp

opp

adj

opp

hyp

hyp

- Use your calculator to answer to 4 decimal places (a) cos 25° (b) sin 50° (c) tan 34°

- Use your calculator to answer to 4 decimal places (a) cos 25° (b) sin 50° (c) tan 34°
- (a) cos 25 = 0.906307787
= 0.9063

- (b) sin 50 = 0.766044443
= 0.7660

- (c) tan 34 = 0.674508516
= 0.6745

- Use your calculator to find the angles to the nearest degree
(a) sin A = 0.83 (b) cos B = ¾ (c) tan A = 5/7

- Use your calculator to find the angles to the nearest degree
(a) sin A = 0.83 (b) cos B = ¾ (c) tan A = 5/7

- (a) 2ndF, sin, .83 = 56.098738 = 56°
- (b) 2ndF, cos, a/b, 3 ↓ 4 = 41.40962211 = 41°
- (c) 2ndF, tan, a/b, 5 ↓ 7 = 35.53767779 = 36°

- In the triangle below, find the length of b
- The side we must find is the adjacent (b)
- We have the hypotenuse c = 10m
- The ratio that uses adj. & hyp. is cos
- So cos 60° = =
- 0.5 =
- b = 10(0.5)
- b = 5m Answer

adjacent

hypotenuse

b

10

b

10

c = 10m

a

60°

b

- Find the angle A to the nearest degree
- We have the opposite & the adjacent so we use tan ratio
- Tan A = =
- Tan A =
- Use calculator 2ndF, tan, a/b, 4 ↓ 3 =
- A = 53.1301
- A = 53° Answer

Opposite

adjacent

4

3

4

3

A°

3m adjacent

4m opposite

- Find the side c (hyp.) to 2 decimal places
- We are given angle & opposite to find hyp.
- sin 40° =
- 0.6428 =
- 0.6428 x c = 15
- c =
- c = 23.34 Answer

15

c

15

c

15

0.6428

c

15m

40°

b

- Given a section through a roof with 2 unequal pitches, calculate
(a) the rise of the roof

(b) the length of rafter c

(c) the span b

5.42m

c

40°

30°

b

- This question may seem complicated but we can simplify it by using our knowledge of right-angle triangles
- Firstly, divide triangle into 2 right-angled triangles (using the rise line)

5.42m

c

rise

40°

30°

b

- On the larger triangle we have the angle 30° & the hypotenuse 5.42m so we can use ratio sin 30° to find the opposite (rise)
Sin = (soh)

opposite

hypotenuse

5.42m

c

40°

30°

b

opposite

hypotenuse

- Sin 30°=
- 0.5 =
- 0.5 x 5.42 = rise
- rise = 2.71m Answer (a)

rise

5.42

5.42m

c

40°

30°

b

- So on the smaller triangle we now have the opposite (2.71m) and the angle 40°
- So to find adjacent (part of span) we use Tan
Tan 40° =

0.839 =

0.839 x adj. = 2.71

adj. = 2.71 ÷ 0.839

= 3.23m

Opposite

adjacent

2.71

adjacent

5.42m

c

40°

30°

b

adj.

- Using Pythagoras we can find c
- a² + b² = c²
- 2.71² + 3.23² = c²
- 7.3441 + 10.4329 = c²
- c² = 17.777
- c = √17.777
- c = 4.216m Answer (b)

5.42m

c

2.71m

40°

30°

3.23m

b

- Using Pythagoras we can find the rest of the span i.e. the base of the larger triangle
- a² + b² = c²
- 2.71² + b² = 5.42²
- 7.344 + b² = 29.376
- b² = 29.376 – 7.344
- b² = 22.032
- b = √22.032
- b = 4.694m

5.42m

c

2.71m

40°

30°

b

3.23m

So 4.694 + 3.23 = span

Span = 7.924m Answer (c)

5.42m

c

2.71m

40°

30°

b

3.23m