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4.015 Exact value triangles

Worksheet
Exact values
1

Write down the exact value of the following:

a

\sin 60 \degree

b

\cos 60 \degree

c

\tan 30 \degree

d

\sin 45 \degree

2

Given that \sin \theta = \dfrac{1}{2} in a right triangle:

a

State the value of \theta.

b

Hence, find \cos \theta.

3

Find the exact value of the pronumeral(s) in the following triangles:

a
b
c
d
e
f
g
h
i
j
4

Use exact values to solve for \theta in the following triangles:

a
b
5

Consider the following diagram:

a

If \angle EBA is 60 \degree, name two other angles that are also 60 \degree.

b

Given that CD has a length of 5 \sqrt{7}, calculate the exact values of m \text{ and }n.

6

Consider the figure shown:

a

Find the exact length of the following:

i

p

ii

q

iii

r

iv

s

b

Hence, find the exact perimeter of the quadrilateral.

7

Consider the given shape:

a

Find x.

b

Find the exact value of y.

c

Hence, find the exact perimeter of the shape.

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Outcomes

MA11-1

uses algebraic and graphical techniques to solve, and where appropriate, compare alternative solutions to problems

MA11-3

uses the concepts and techniques of trigonometry in the solution of equations and problems involving geometric shapes

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