Similar Triangles, Right Triangles, And The Definition Of The Sine, Cosine And Tangent Functions Of Angles Of A Right Triangle Worksheets With Answer Key Page 13
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43°
500
sin
62
3 .
=
=
a
471
.
41
.
°
sin
69
9 .
Hence,
h = a sin 47.8° = (471.14) sin 47.8° = 349.22 feet.
Problems:
31. A surveyor determines the following information about a triangular shaped piece of property. One
side has length 257.9 feet. A second side has length 185.1 feet. The angle opposite the 185.1 foot
side measures 38.3°. How long is the third side of the property?
32. A merchant ship at its dock in New York was observed to subtend an angle of 6° from the window
of an office 2000 feet from the bow and 3000 feet from the stern of the ship. How long is the ship?
33. A vertical tower is braced by two cables which are anchored to the ground at the same point. At
this point, the angle between the cables is 15°. The first cable is 150 feet long and extends to the
top of the tower. The second cable extends to a point 50 feet below the top of the tower. How long
is the second cable?
34. As an airplane is taking off, its path of ascent makes a 60° angle with the runway. How many feet
does the plane rise while it travels 1200 feet in the air? (Assume the path of the ascent is a straight
line.)
GRAPHING TRIGONOMETRIC FUNCTIONS
Values of the trigonometric functions at 0°, 30°, 45°, 60° and 90° should be memorized. The
following table gives the values.
degrees
radians
sine
cosine
tangent
cosecant
secant
cotangent
0°
0
0
1
0
undefined
1
undefined
π
1
3
3
2
3
30°
2
3
6
2
2
3
3
π
2
2
45°
1
1
2
2
4
2
2
π
1
3
2
3
3
60°
2
3
3
2
2
3
3
π
90°
1
0
undefined
1
undefined
0
2
Example: Using this table (not a calculator) find 2 sin 45° sec 45°.
2
1
°
=
°
=
=
Solution: From the table we have
sin
45
and
sec
45
. 2
Hence,
°
2
cos
45
2
°
°
=
⋅
=
2
sin
45
sec
45
2
2
. 2
2
- 13 -
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