Question

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.

Answer 1

For the hiker whose angle of depression is 37°, you can write:

tan (37°) = 525m / x , where x is the horizontal distance from the hiker to the landmark

=> x = 525 / tan(37) = 696.7m

For the hiker whose angle of depression is 22°, you can write

tan (22°) = 525m / y, where y is the horizontal distance from the hiker to the landmark

=> y = 525m / tan(22) = 1,299.4 m

The distance that separate both hikers is x + y = 696.7 + 1,299.4 = 1,996.1m ≈ 1,996m (rounded to the nearest whole meter)

Answer: 1996m

Answer 2

The hikers are 2064 m apart

The situation forms two right angle triangle.

Right angle triangle:

A right angle triangle has one of its sides as 90 degree.

Therefore,

First hiker distance

tan 37 = opposite / adjacent

tan 37° = 525 / x

x = 525 / tan 37

x = 696.711059326

x = 696. 711 m

Second Hiker distance:

tan 21 = 525 / y

y = 525 / tan 21

y = 1367.68613557

y = 1367.686 m

Distance apart = 696.711 + 1367.686 = 2064.39713557 = 2064 m

learn more on angles of depression here: https://brainly.com/question/10207139