Asked by Kitkat
A surveyor in an airplane observes that the angle of depression to two points on the opposite shores of a lake are 32 and 45 degrees, respectively. What is the width of the lake to the nearest metre, at those two points?
Answers
Answered by
drwls
You need to know the altitude at which the plane is flying. Two angles alone cannot produce a length, no matter what you do to them mathematically. That is a fundamental principle of dimensional analysis.
Answered by
Ethan
I don't know the answer, but I know that in this particular question the plane is flying at an altitude of 9750 metres.( The q. is in Nelson Functions 11 pg.319 #8)
Answered by
DR
1. Label the triangle (point C is where the plane is)
2. Draw a straight line directly down to the lake and call it point D.
3. Find angle c from triangle CAD by subtracting angle 45 from 90 degrees (the three triangles make a 90 degree angle together)
4. Find remaining angles (180-(90+45))
5. Subtract angle a from triangle CAD from 180 to find angle a from triangle ABC
6. Find angle c from triangle ABC by subtracting 45-32 (angles given)
7. Use sine law AAS for triangle ABC(you are given two angles and a side opposite those angles)
b/sinB = c/sinC
9750/sin 32 = c/sin 13
(9750*sin13)/sin32 = c
4138.8 = c
4139 = c
2. Draw a straight line directly down to the lake and call it point D.
3. Find angle c from triangle CAD by subtracting angle 45 from 90 degrees (the three triangles make a 90 degree angle together)
4. Find remaining angles (180-(90+45))
5. Subtract angle a from triangle CAD from 180 to find angle a from triangle ABC
6. Find angle c from triangle ABC by subtracting 45-32 (angles given)
7. Use sine law AAS for triangle ABC(you are given two angles and a side opposite those angles)
b/sinB = c/sinC
9750/sin 32 = c/sin 13
(9750*sin13)/sin32 = c
4138.8 = c
4139 = c
Answered by
bob
I got the same answer as @DR but textbook says 7499m
Answered by
Kennnn
I got the same answer as @DR as well. The textbook has a misprint.
Answered by
m
i also got 4139
Answered by
K
i got the same answer
Answered by
MY
Yes, the answer is 4139 m.
Answered by
Anonymous
Why did you chose the 45 degree angle instead of the 32 degree angle? Shouldn't it be the 32 degree angle because that's the angle that corresponds to that new triangle we made??
Answered by
Anonymous
no
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