Right Triangle Trig: Solving for a Missing Side
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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
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