1. sine Trigonometry cosine adjacent Ө Tangent Right Angle
Sample Questions & Solutions
Tangent
cosine
sine
adjacent
Right Angle Ө

2. Pythagoras Theorem
Given a = 3.25m & b = 3.45m calculate the length of c
a² + b² = c²
3.25² ² = c²
= c²
= c²
c = √22.466
c = 4.74m Answer c a b

3. Question
Copy each of the triangles below and label each of the sides and the angle.
(c) A
(b) A A
(a)
(e) A
(f) A
(d) A

4. Answer
Copy each of the triangles below and label each of the sides and the angle.
(c) A
(b) A A
(a)
hyp
adj
opp
hyp
opp
opp
hyp
adj
(e) A
adj
adj
(f) A
adj
(d) A
opp
hyp
adj
opp
opp
hyp
hyp

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

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

7. Question 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

8. Answer 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°
(b) 2ndF, cos, a/b, 3 ↓ 4 = = 41°
(c) 2ndF, tan, a/b, 5 ↓ 7 = = 36°

9. Solving Right-angle Triangles
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

10. Solving Right-angle Triangles
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 =
A = 53° Answer
Opposite
adjacent 4 3 4 3 A°
3m adjacent
4m opposite

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

12. Solving Right-angle Triangles
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

13. Solving Right-angle Triangles
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

14. Solving Right-angle Triangles
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

15. Solving Right-angle Triangles
Sin 30°=
0.5 =
0.5 x 5.42 = rise
rise = 2.71m Answer (a)
opposite
hypotenuse
rise
5.42
5.42m c
40°
30° b

16. Solving Right-angle Triangles
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
30°
40° b
adj.

17. Solving Right-angle Triangles
Using Pythagoras we can find c
a² + b² = c²
2.71² ² = c²
= c²
c² =
c = √17.777
c = 4.216m Answer (b)
5.42m c
2.71m
40°
30° b
3.23m

18. Solving Right-angle Triangles
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
b² =
b² = – 7.344
b² =
b = √22.032
b = 4.694m
5.42m c
2.71m
40°
30° b
3.23m

19. Solving Right-angle Triangles
So = span Span = 7.924m Answer (c)
5.42m c
2.71m
40°
30° b
3.23m