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Math-2ALesson 7-8
Trigonometric Ratios for Right Triangles
Quiz
a
AC
B
35°
15
1. Use SOHCAHTOA to solve for ‘a’.
2. Solve for ‘c’
Solve a triangle: finding the unknown
measures of angles and sides.
Vocabulary6
x
7
A
Solving this triangle required no trigonometry.
90 BmAm
B
222 76 x
13x
59º
C
9059 Bm
31Bm
222 cba
4936 2 x
132 x90Cm
Solve the Triangley
x
12
A
90 BmAm
B
38º
C9038 Bm42Bm
1238sin
y
42º
y38sin12 4.7
y=7.4
hyp
oppA sin
y
x
12
A
B
38º
C
42ºy=7.4
1238cos
x
x38cos12 5.9 x=9.5
Solve the Triangley
x
27
A
90 BmAm
B
18º
C9018 Bm62Bm
2718sin
y
62º
y38sin27 6.16
y=16.6
hyp
oppA sin
y
x
27
A
B
18º
C
62ºy=16.6
2738cos
x
x38cos27 3.21 x=21.3
Solve the Triangle5
x
c
A
90 BmAm
B
25º
C9025 Bm65Bm
c
525sin
90Cm
65º
8.11
c=11.8
hyp
oppA sin
525sin
1 c c
25sin
5
5
x
c
A
B
25º
C
65ºc=11.8
8.1125cos
x
x25cos8.11 7.10 x = 10.7
565tan
x
x65tan5 7.10
Vocabulary
Angle of Elevation: angle above the horizon that the
eye has to look up to see something.
Angle of Depression: angle below the horizon that the
eye has to look down at something.
Using Angle of ElevationThe angle of elevation from the buoy to the top of the
Barnegat Bay lighthouse 130 feet above the surface of the
water is 5º. Find the distance x from the base of the
lighthouse to the buoy.
130
x
5º
1. Draw the picture
2. Write the equation.x
130)5tan(
3. Solve for the unknown variable.
ftx 9.148585tan130
130)85tan(
x
If the height of a building is 470 m and you are
standing 100 m away from the building, find the
angle of elevation to the top of the building.
1. Draw the picture
2. Write the equation.
3. Solve for the unknown variable.
470
100
xº
100
470)tan( x
x
100
470tan 1 78
What is the height of a tree if you are standing 50
feet from it, and that angle of elevation (from
your height of eye) is 40 degrees. Assume that
your eyes are 5 feet above the ground.
1. Draw picture 2. Write equation.
3. Solve for the variable.
x
50 ft
40º
5 ft5 ft
50)40tan(
x
x)40tan(50 ft42
4. Answer the question.
height
of tree ft47
