Trigonometry 2.Finding Sides Of Triangles.

L

Adj’

Hyp’

21m

23o

2123cos

Lo

hyp

adjxo cos

…………….

Finding The Unknown Side.Consider the triangle below:

35o

14m

Find the length of side L.

L

(1) Identify the two sides of the triangle.

Opp

Hyp’

(2) Choose the correct trig’ ratio.

hyp

oppxo sin

(3) Substitute the values into the ratio.

1435sin

Lo

(4) Calculate the sine value to 3d.p .

141

574.0 L

(5) Cross multiply and solve for L.

574.014L

04.8L

L = 8.04m to 2d.p .

S O H C A H T O A

Example 2.Consider the triangle below:

Find the length of side L.

L

(1) Identify the two sides of the triangle.

Adj’

Hyp’

(2) Choose the correct trig’ ratio.

(3) Substitute the values into the ratio.

(4) Calculate the cosine value to 3d.p .

(5) Cross multiply and solve for L. L = 19.34m to 2d.p .

21m

23o

2123cos

Lo

211

921.0 L

921.021L

34.19L

hyp

adjxo cos

S

O

H

C

A

H

T

O

A

What Goes In The Box ?

(1) Identify the two sides of the triangle.

(2) Choose the correct trig’ ratio.

(3) Substitute the values into the ratio.

(4) Calculate the trig’ angle value to 3d.p .(5) Cross multiply and solve for L to 1 d.p

74o

W

4.6cm

(1)

(1)

(2)

(3)

(4)

(5)

opp

adj

adj

oppxo tan

6.474tan

Wo

6.41

49.3 W

6.449.3 W

05.16W

W = 16.1cm to 1 d.p.

Calculate side W below.

Harder Example.The example below is trickier when it comes to the cross multiplication.

34o

L

24.6m

(1) Identify the two sides of the triangle.

(2) Choose the correct trig’ ratio.

(3) Substitute the values into the ratio.

(4) Calculate the trig’ angle value to 3d.p .(5) Cross multiply and solve for L to 1 d.p

hyp’

adj’

hyp

adjxo cos

Lo 6.24

34cos

L

6.24

1

829.0

6.24829.0 L

829.0

6.24L

L = 29.67m to 2.d.p.

What Goes In The Box? 2Find the length of the unknown sides below:

(1) 14cm

A25o

(2)

2.1m

B

56o

(3)

13.9m

C

42o

(4)

8.3m D18o

5.9cm

3.11m

9.3m 8.73m