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Middle Years

6.03 Trigonometric ratios

Worksheet
Right-angled triangles
1

For the following triangles, name the hypotenuse:

a
b
2

Consider the following triangle:

a

State the opposite side to angle \theta.

b

State the adjacent side to angle \theta.

c

State the opposite side to angle \alpha.

d

State the adjacent side to angle \alpha.

e

State the angle that is opposite the hypotenuse.

3

With reference the angle \theta, find the value of these ratios for each of the following triangles:

i

\dfrac{\text{Opposite }}{\text{Adjacent }}

ii

\dfrac{\text{Opposite }}{\text{Hypotenuse }}

iii

\dfrac{\text{Adjacent }}{\text{Hypotenuse }}

a
b
c
d
e
f
Trigonometric ratios
4

Write down the indicated ratios for the following triangles:

a
i

\tan \theta

ii

\sin \alpha

b
i

\sin \theta

ii

\tan \alpha

c
i

\cos \theta

ii

\cos \alpha

d
i

\tan \theta

ii

\sin \alpha

e
i

\cos \theta

ii

\tan \alpha

f
i
\sin \theta
ii
\cos \alpha
5

Consider the following triangle:

a

Find the value of x.

b

Find the value of \sin \theta.

c

Find the value of \cos \theta.

6

Consider the following triangle:

a

Find the value of x.

b

Hence, find the value of \tan \theta.

Unknown sides
7

For the following triangle, if \tan \theta = \dfrac{2}{3}, find the value of b.

8

For the following triangle, if \tan \theta = \dfrac{4}{3}, find the value of d.

9

For the following triangle, if \tan \theta = 0.4, find the value of b.

Round your answer correct to one decimal place.

10

Find the value of the pronumeral in the following triangles, correct to two decimal places:

a
b
c
d
Unknown angles
11

Given the following triangle, calculate the exact value of \tan \theta.

12

For each of the following triangles, find the value of x to the nearest degree:

a
b
13

An isosceles triangle has equal side lengths of 10 \text{ cm} and a base of 8 \text{ cm} as shown.

Calculate the size of angle A to one decimal place.

14

Find the value of \tan \theta for the following triangle:

Applications
15

Find the value of the pronumeral(s) in the following diagrams, correct to the nearest whole number:

a
b
c
d
e
16

If d is the distance between the base of the wall and the base of the ladder, find the value of d to two decimal places.

17

A ladder is leaning at an angle of 44 \degree against a 1.36 \text{ m} high wall. Find the length of the ladder, to two decimal places.

18

A ladder measuring 2.36 \text{ m} in length is leaning against a wall.

If the angle the ladder makes with the ground is y \degree, find the value of y to two decimal places.

19

A girl is flying a kite that is attached to the end of a 23.4 \text{ m} length of string. The angle between the string and the vertical is 21 \degree. The girl is holding the string 2.1 \text{ m} above the ground.

a

Find x, correct to two decimal places.

b

Hence, find the height, h, of the kite above the ground, correct to two decimal places.

20

In the diagram, a string of lights joins the top of the tree to a point on the ground 23.9 \text{ m} away. If the angle that the string of lights makes with the ground is \theta \degree, find \theta to two decimal places.

21

A ladder measuring 1.65 \text{ m} in length is leaning against a wall. If the angle the ladder makes with the wall is y \degree, find y to two decimal places.

22

Find the value of \tan \theta in the following trapezium:

23

A sand pile has an angle of 40 \degree and is 10.6 \text{ m} wide.

Find the height of the sand pile, h, to one decimal place.

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