Two hikers on opposite sides of a canyon each stand precisely 525 meters above the canyon floor. They each sight a landmark on the canyon floor on a line directly between them. The angles of depression from each hiker to the landmark meter are 37° and 21°. How far apart are the hikers? Round your answer to the nearest whole meter.

Question

campbell_st · Answer

here is the initial picture

|dw:1352000375351:dw|

there are lots of ways of doing this... But I'll use right angle trig... you can use sine rule, cosine rule... but both need a little work 1st

Hiker 1:

find the horizontal distance to the landmark

|dw:1352000616011:dw|

find d    

$$\tan(53) = \frac{d}{525}$$

solve for d

similar process for hiker 2. 

except the angle won't be 53.... I'll leave that for you to find. 

Last task, add the 2 distances together to get the total distance between Hiker 1 and Hiker 2