topic badge
AustraliaNSW
Stage 5.1-2

8.03 Finding a side

Worksheet
Evaluate trigonometric functions
1

Evaluate the following to two decimal places:

a

\sin 82 \degree

b

\cos 28 \degree

c

\tan 84 \degree

d

9 \sin 63 \degree

e

7 \cos 77 \degree

f

8 \tan 28 \degree

g

\dfrac{\sin 71 \degree}{7}

h

\dfrac{\cos 7 \degree}{9}

i

\dfrac{\tan 52 \degree}{7}

Unknown sides
2

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

a
b
c
d
e
f
g
h
i
j
3

Find the value of g in the following triangle, correct to two decimal places:

4

Find the value of f, correct to two decimal places.

5

Find the value of h, correct to two decimal places.

6

Find the value of h in the following figure, correct to the nearest integer.

Applications
7

A lighthouse is positioned at point A and a boat is at point B in the given diagram:

Find the length of AB to two decimal places.

8

In the following diagram, Neil's home is located at point A, and Neil is standing at point B.

If d is the distance between Neil and his home, find the value of d correct to two decimal places.

9

Consider the following diagram:

a

Find x correct to two decimal places.

b

Find w correct to one decimal place.

c

Find z correct to the nearest whole number.

10

Sally measures the angle of elevation to the top of a tree from a point 20 \text{ m} away to be 43 \degree.

Find the height of the tree, h, to the nearest whole number.

11

Two flag posts of height 12 m and 17 m are erected 20 m apart.

Find the length, l, of the string needed to join the tops of the two posts. Round your answer to one decimal place.

12

Consider the diagram shown:

a

Find the length of AD, correct to two decimal places.

b

Find the length of BD, correct to two decimal places.

c

Hence, find the length of AB, correct to two decimal places.

13

In the given diagram:

AB is a tangent to a circle with centre O.

OB is 24 \text{ cm} long and cuts the circle at C.

a

Find the radius of the circle, r, correct to one decimal place.

b

Find the length of BC to the nearest centimetre.

14

Find the value of x, the side length of the parallelogram, to the nearest centimetre.

Sign up to access Worksheet
Get full access to our content with a Mathspace account

Outcomes

MA5.1-10MG

applies trigonometry, given diagrams, to solve problems, including problems involving angles of elevation and depression

What is Mathspace

About Mathspace