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6.01 The trigonometric ratios

Worksheet
Sides of a right-angled triangle
1

For the following triangles, state which side is the hypotenuse:

a
b
c
d
2

For the following triangles, state the angle which is opposite the hypotenuse:

a
b
c
d
3

For the following triangles, with reference angle \theta, identify:

i

The adjacent side

ii

The opposite side

a
b
c
d
4

Identify the reference angle in each of the following triangles given the labelled side:

a
b
c
d
5

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

Identify the angle that is opposite the hypotenuse.

Trigonometric ratios
6

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
7

For the following triangles, determine \cos \theta:

a
b
8

Evaluate \sin \theta in the following triangles:

a
b
9

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

a
b
10

Which trigonometric ratio relates the given sides and reference angle in the following triangles?

a
b
c
d
11

For each of the following triangles:

i

Find the value of x.

ii

Hence find the value of \sin \theta.

iii

Hence find the value of \cos \theta.

a
b
12

For each of the following triangles:

i

Find the value of the missing side.

ii

Find the value of \tan \theta.

a
b
c
13

In the following triangle \sin \theta = \dfrac{4}{5}:

a

Which angle is represented by \theta?

b

Find the value of \cos \theta.

c

Find the value of \tan \theta.

14

In the following triangle \tan \theta = \dfrac{15}{8}.

a

Which angle is represented by \theta?

b

Find \cos \theta.

c

Find \sin \theta.

15

Write down the following ratios for the given triangle:

a
\sin \theta
b
\sin \alpha
c
\cos \theta
d
\cos \alpha
e
\tan \theta
f
\tan \alpha
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VCMMG319

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

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