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Problem Solving with Trigonometry
Do the following when solving trigonometry word problems…
1. Draw a picture.2. Decide which trigonometry formula you must
use.3. Solve the word problem.
SOH – CAH – TOA LAW OF SINES
LAW OF COSINES SAS TRIANGLE AREA
cCsin
bBsin
aAsin
Ccosab2bac 222 Csinab21
A
Right Triangle Ratios
A large helium balloon is tethered to the ground by two taut lines. One line is 100 feet long and makes an 80° angle with the ground. The second line makes a 40° angle with the ground. How long is the second line, to the nearest foot? How far apart are the tethers?
80° 40°
100 ft x
x80sin
10040sin
80sin10040sinx
40sin80sin100
x
x = 153 ft
60°y = 135 ft
y60sin
10040sin
60sin10040siny
40sin60sin100
y
y
A ship’s sonar locates a treasure chest at a 12° angle of depression. A diver is lowered 40 meters to the ocean floor. How far (to the nearest meters) does the diver need to swim along the ocean floor to get the treasure chest?
12°
12°40 m
x
x40
12tan
4012tanx
12tan40
x
x = 188 m
Farmer Joe needs to fence his triangular plot of land for his cows. The angle between two sides measures 83°. One side
is 122 ft and the other is 215 ft. How much fencing does farmer Joe need to the nearest foot? What is the area of his
plot of land?
83°
122
ft
215 ft
x
83cos2151222215122x 222
73.715,54x 2 234x
234 ft
215122234 571 ft
83sin)215)(122(21
Area
Area = 13017 ft2
Homework
Mixed Trig Application Problems Worksheet