Solve the following problems using the method above.
1. Obiwan is standing at a distance of 15m from the base of the tree. From where he is standing, he can see the top of the tree. If the tree is 15m and Obiwan is 1m tall, what is the angle of elevation of the top of the tree?
2. A bamboo pole is leaning against a tree. If the height of the tree is 12.2 meters and the angle made by the pole and the ground is 40°, what is the length of the pole?
3. According to a lighting specialist for an art gallery, for best illumination of a piece of art, it is recommended that a ceiling-mounted light be 1.8 m from the piece of the art and the angle of depression of the art piece be 380, How far from the wall should the light be placed so that the recommendations of the specialist are met? Give your answer to the nearest tenth of a meter.
1. Obiwan is standing at a distance of 15m from the base of the tree. From where he is standing, he can see the top of the tree. If the tree is 15m and Obiwan is 1m tall, what is the angle of elevation of the top of the tree?
2. A bamboo pole is leaning against a tree. If the height of the tree is 12.2 meters and the angle made by the pole and the ground is 40°, what is the length of the pole?
3. According to a lighting specialist for an art gallery, for best illumination of a piece of art, it is recommended that a ceiling-mounted light be 1.8 m from the piece of the art and the angle of depression of the art piece be 380, How far from the wall should the light be placed so that the recommendations of the specialist are met? Give your answer to the nearest tenth of a meter.
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Answer:
1.Hi there,
Consider the problem as a right
angled triangle.
The tree meeting the ground is the right angle.
Obiwan's line of sight to the top of the tree
is the hypotenuse.
The height of the tree minus Obiwan's height
is the opposite side (in this case)
The distance between Obiwan and the tree is the
adjacent side.
Using the opposite side's size (15m - 1m) = 14m
and the adjacent side = 15m
tan(x) = opposite/adjacent
tan(x) = 14/15
tan(x) = 0.93
tan^-1 (0.93) = 43 degrees.
This is Obiwan's angle of elevation.
Hope this helps :-)
2.Cos40° = 12.2/hh= 12.2/cos40h= 18.98 meters, approximately 19 meters. Therefore, the length of the pole is 18.98 or approximately 19 meters.
3. 1.418419356 meters
cos(38)=adj/hype=x/1.8
x=1.8 cos (38)=1.418419356 meters
x=1.418419356 meters