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Solve for Missing Sides of a Right Triangle using Trig Ratios
Contributed by: Miles
(Original author: Pappal)
In this activity you will use your knowledge of the three
main trig ratios to solve for missing sides of right triangles.
Recall the three main trig ratios.
tangent =
cosine =
Sine  = 
hypotenuse
hypotenuse
opposite
adjacent
adjacent
opposite
Drag and drop the correct values to show each trig ratio.
tangent =
cosine =
Sine = 
hypotenuse
?
hypotenuse
opposite
adjacent
?
opposite
?
adjacent
Drag and drop each trig function with the correct ratio.
Answer carefully!
tangent
?
cosine
?
sine
?
=
=
=
hypotenuse
adjacent
hypotenuse
opposite
adjacent
opposite
Recall, these formulas can be remember by using
C stands for cosine
S stands for sine
T stands for tangent
SOH
CAH
TOA
A stands for adjacent
O stands for opposite
H stands for hypotenuse
Each of these triangles has a right angle
Next, you have to be able to label the right triangle.
and an acute angle that is marked.
Here are two example triangles
The last side is the adjacent, next to the marked angle
The opposite is the side across from the marked angle
The hypotenuse is the side across from the right angle
Next, you have to be able to label the right triangle.
Here are two example triangles
Hyp
Opp
Adj
Adj
Hyp
Opp
Drag and drop the values onto the right triangle diagram.
Hyp
?
Opp
?
Adj
?
Solve for "x" in the right triangle using a trig ratio.
Consider how you would solve this problem.
35
9
x
Drag and drop the correct values in reference to the 
35º angle.
First, look at the sides involved in the problem
hypotenuse
?
adjacent
?
35
9
x
opposite
?
Which trig ratio should we use to solve for "x"?
sine
cosine
tangent
Hyp
35
9
Adj
x
Opp
Write an equation involving sine of 35º to solve for x.
sin 35 =
Hyp
35
9
Adj
x
Opp
Use algebra skills to solve for x. 
sin 35 =
x
9
35
9
x
x = 9 ÷ (sin 35)
x = 9 + sin(35)
x = 9*sin(35)
Use a calculator to solve for x.  
Round to the nearest hundredth.
sin 35 =
x
9
35
9
x
x = 
x = 9*sin(35)
units
sine
cosine
tangent
Which Trig Ratio should you use to solve for x?
15
3
x
Which Trig Ratio should you use to solve for x?
20
75
x
sine
cosine
tangent
sine
cosine
tangent
Which Trig Ratio should you use to solve for x?
77
x
3
Solve for x in this right triangle.  
First label the sides in relation to the 70º angle.
Hyp
?
Opp
?
x
6
70
Adj
?
Choose the trig ratio
sine
cosine
tangent
Hyp
Opp
x
6
70
Adj
Write an equation to solve for x.
sin
=
Hyp
Opp
6
?
x
?
x
6
70
Adj
Rewrite the equation to solve for x.
sin
70
=
6
x
Hyp
Opp
x
x = 6*sin(70) 
x = 6/(sin70)
x = 6 + sin(70)
6
70
Adj
Solve for x. (Round to the nearest tenth.)
x = 6 / (sin70)
sin 70 = 6 / x
Hyp
Opp
x
6
70
x =
Adj
units
Solve for x in this right triangle. 
First label the sides in relation to the 75º angle.
Opp
?
Hyp
?
9
75
x
Adj
?
Choose the correct trig ratio.
Opp
Hyp
9
75
x
Adj
sine
cosine
tangent
Write an equation. Then solve for x.
cos
Opp
Hyp
=
9
x
?
9
?
75
x
Adj
Solve for x. 
Round to the tenths place.
x = 
units
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