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Right Triangle Trigonometry Activity
We name the sides of a right triangle in relationship to one of the non-90° angles, θ:
OPPOSITE (the leg furthest
from the marked angle)
ADJACENT (the leg next to
the marked angle)
HYPOTENUSE (the side
furthest from the right angle)

New definitions for the trig function:
sine
cosecant
opp
sin( ) 
hy p
csc( ) 
cosine
secant
adj
cos  
hy p
sec( ) 
tangent
cotangent
sin( ) opp
tan  

cos( ) adj
cot( ) 
1
hy p

sin( ) opp
1
hy p

cos( ) adj
1
adj

tan( ) opp
You can use the inverse of sine - written as sin-1(x) or as arcsin(x) - to find an angle if you know the sides called
opposite and hypotenuse on the triangle.
sin()
 (the angle)
-1
OPP
sin (HYP
)
Similarly, cosine and tangent have inverses.
Advice for rounding numbers in this class and all math classes: never round a number before the end of a
problem -- it leads to errors!
In-Class Examples: Solve the following triangles (use exact values until the last calculation wherever possible,
round answers to the nearest hundredth):
90 cm
o
20
8 ft
35
o
540 in.
90 in.
Right Triangle Trig Problems: (18 points) NAME
 For each triangle, solve for all the missing sides and angles.
 All angles are in degrees.
 Make sure you use the degree symbol, appropriate units, and round to the nearest 100th.
 Show work to the right side. Write the answers in the appropriate location on each triangle:
WORK:
25 cm
(1)
o
39
(2)
14 cm
11 cm
(3)
2.31 m
o
20
(4)
90 cm
540 cm
(5)
65"
72"
(6)
120 cm
o
65
h=
This is an isosceles triangle. Also
find h, the height