Right Triangle Trig: Solving for a Missing

Side

Trigonometric RatiosWe define the 3

trigonometric ratios in terms of fractions

of sides of right angled triangles.

Hypotenuse

(HYP)

Adja

cent

(AD

J)

Opposite (OPP)

SohCahToaSine equals Opposite over HypotenuseCosine equals Adjacent over HypotenuseTangent equals Opposite over Adjacent

Practice Together:Given each triangle, write the ratio that could be used to find x by connecting the angle and sides given.

65 a

x

32

bx

YOU DO:Given the triangle, write all the ratios that could be used to find x by connecting the angle and sides given.

56

d

x

c

Steps to finding the missing sides of a right triangle using trigonometric ratios:

1. Redraw the figure and mark on it HYP, OPP, ADJ relative to the given angle

61 9.6 cm

x

HYP

OPP

ADJ

Steps to finding the missing sides of a right triangle using trigonometric ratios:

2. For the given angle choose the correct trigonometric ratio which can be used to set up an equation

3. Set up the equation

61 9.6 cm

x

HYP

OPP

ADJ

Steps to finding the missing sides of a right triangle using trigonometric ratios:

4.Solve the equation to find the unknown.

61 9.6 cm

x

HYP

OPP

ADJ

Practice Together:Find, to 2 decimal places, the unknown length in the triangle.

41

x m7.8 m

YOU DO:Find, to 1 decimal place, all the unknown angles and sides in the triangle.

a m

14.6 m

63

b m

Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth.

5520 m

x

20

55tanx

m 6.28x

x55tan20tan

20 55

)

Shrink yourself down and stand where the angle is.

Now, figure out which trig ratio you have and set up the problem.

Ex: 2 Find the missing side. Round to the nearest tenth.

72

80 ft

x

x

8072tan

ft 26x

8072tan x

72tan

80x

tan

80 72

= ( ) )Shrink yourself down and stand where the angle is.

Now, figure out which trig ratio you have and set up the problem.

Ex: 3 Find the missing side. Round to the nearest tenth.

24

283 mx 283

24sinx

m 1.115x

x24sin283Shrink yourself down and stand where the angle is.

Now, figure out which trig ratio you have and set up the problem.

Ex: 4 Find the missing side. Round to the nearest tenth.

4020 ft x

2040cos

x

ft 3.15x

x40cos20