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3.03 Sides and angles of right-angled triangles

Worksheet
Unknown side lengths
1

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
2

Consider the following triangle:

a

Complete the equation: \cos x = \dfrac{⬚}{⬚}.

b

Substitute \cos x = 0.75 into your equation.

c

Solve your equation to find the value of b.

3

Consider the following triangle:

a

Complete the equation: \tan \theta = \dfrac{⬚}{⬚}.

b

Substitute \tan \theta = 0.4 into your equation.

c

Solve your equation to find the value of b. Round your answer to one decimal place.

4

Consider the following triangle:

a

Complete the equation: \sin x = \dfrac{⬚}{⬚}.

b

Substitute \sin x = \dfrac{4}{5} into your equation.

c

Solve your equation to find the value of b.

5

Consider the following triangle:

a

Complete the equation: \tan \theta = \dfrac{⬚}{⬚}.

b

Substitute \tan \theta = \dfrac{2}{3} into your equation.

c

Solve your equation to find the value of b.

6

Consider the given diagram:

a

Write a trigonometric equation that can be solved for b.

b

Find the value of b to one decimal place.

7

Consider the following triangle:

a

Find an expression for \tan x.

b

If x = 39 and a = 10, solve for b, rounding your answer to one decimal place.

8

Consider the following diagram:

Calculate the value of a, to the nearest centimetre.

9

Consider the following diagram:

a

Which trigonometric ratio could be used to find the value of x?

b

Find the value of x. Round your answer to two decimal places.

c

Find the value of h. Round your answer to the nearest integer.

10

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

Unknown angles
11

Find the acute angle \theta to the nearest degree:

a
\sin \theta = 0.1
b
\cos \theta = 0.73
c
\tan \theta = 1.3
d
\cos \theta = \dfrac{4}{9}
e
\tan \theta = \dfrac{4}{9}
f
\sin \theta = \dfrac{35}{45}
g
\cos \theta = 0.5216
h
\tan \theta = 2.694
i
\sin \theta = 0.7458
12

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

a
b
c
d
e
f
13

For the following triangles, find the value of \theta to the nearest degree:

a
b
c
d
14

Consider the given figure:

Find the following pronumerals, rounding your answers to two decimal place:

a

x

b

y

c

z

15

Consider the following figure:

Find the following, rounding your answers to two decimal place:

a

x

b

y

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Outcomes

ACMEM117

apply the tangent ratio to find unknown angles and sides in right-angled triangles

ACMEM119

apply the cosine and sine ratios to find unknown angles and sides in right-angled triangles

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