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6.02 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.

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Outcomes

VCMMG319

Use similarity to investigate the constancy of the sine, cosine and tangent ratios for a given angle in right-angled triangles.

VCMMG320

Apply trigonometry to solve right-angled triangle problems.

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