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?

Question

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?

DR · Accepted Answer

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

bob · Answer

I got the same answer as @DR but textbook says 7499m

Ethan · Answer

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)

Kennnn · Answer

I got the same answer as @DR as well. The textbook has a misprint.

m · Answer

i also got 4139

Anonymous · Answer

no

K · Answer

i got the same answer

MY · Answer

Yes, the answer is 4139 m.

Anonymous · Answer

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??

drwls · Answer

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.