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 12
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43Problems:
26. Solve ∆ABC with b = 33, c = 15 and A = 102°.
27. Solve ∆ABC with a = 2, b = 3 and c = 7.
28. Find angle R in ∆PQR where p = 53, q = 101 and r = 95.
29. Solve ∆PAS with p = 7, a = 25 and s = 24.
30. Solve ∆ABC with a = 7, b = 7 and c = 7.
NARRATIVE PROBLEMS
In the following examples and problems it is important that you
1. read the problem carefully,
2. draw a reasonable sketch of the situation,
3. identify and label the known and the unknown quantities,
4. write an equation relating the known and unknown quantities,
5. solve the equation and
6. examine the reasonableness of your answer as it relates to the sketch.
Example: The Washington Monument casts a shadow
793 feet long when the angle of elevation of
the sun is 35°. How tall is the monument?
(Assume the ground is level, though you may
know differently.)
Solution: From the sketch as shown in Figure T23,
x
°
=
Figure T23
tan
35
.
793
Hence
=
°
=
x
793
tan
35
555
.
26
feet.
Example: Two men, 500 feet apart on level ground, observe a hot-air balloon between them. The
respective angles of elevation are measured as 62.3° and 47.8°. What is the altitude of
the balloon above the ground level?
h
=
=
°
Solution: Since
sin
C
,
h
a
sin
47
8 .
a
We need to find side a. By the Law of Sines,
a
b
=
.
sin A
sin B
Since B = 180° - (62.3° + 47.8°) = 69.9°, we get
a
500
=
.
°
°
sin
62
3 .
sin
69
9 .
Thus,
Figure T24
- 12 -
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