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UNIT 6 : BASIC
TRIGONOMETRY WITH TRIANGLES
LESSON 5: PROBLEM SOLVING
Right
Triangles Problems:
Example 1:
John is
standing 12 m from the base of a cedar tree in his backyard. The angle
of elevation of the
top of the tree is 480.
calculate the height of the tree.
Solution: The angle between the horizontal and the line of sight
(AB) of the top of the tree is the ANGLE OF ELEVATION ( <ABC in diagram)
A h B C 12 m Angle of elevation = 480
Example 2:
From the
top of a cliff 15 m high, the angle of depression of a sailboat on the lake is
350. Find the distance of
the boat from the cliff.
Solution: The angle between the horizontal (dashed line AD) and
the line of sight (AC) of the boat is the ANGLE OF DEPRESSION ( <DAC in
diagram)
A
D
)Angle of depression =
350
15 m
B x C
Oblique
Triangle Problems.
Example 3:
Find the
distance up the slope DE of the mountain if the angles of elevation of the peak
from directly opposite sides of the mountain are 480 and 540. The distance EF is 900 m.
D
f
480 540
E 900
m F
Solution:
First
find the measure of < D: 180o – (48o + 54o)
= 78o
Now find
f using the sine law. This is the
AAS case.
Example 4:
Paul
travels due east at 90 km/h for 3 hours.
George travels N300E at 110 km/h for 2 ½ hours. How far apart are they if they started from
the same location?
Solution:
Paul travels a distance of 90 x 3 = 270 km.
due east. George travels 110 x 2.5 =
275 km at an angle of 600 to Paul’s path.
N G
275
300
E
S 270 P
This is the SAS case. Use the cosine law for side GP.