Two hikers on opposite sides of a canyon each stand precisel

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 degree and 21 degree. How far apart are the hikers? Round your answer to the nearest whole meter. A. 1064 m B. 2065 m C. 2063 m D. 2064 m

Solution

Solution:

let;

x = horizontal distance of the first hiker from the landmark

and

y = horizontal distance of the second hiker from the landmark

For the first hiker,

tan 37 = 525/x

=> x = 525/tan 37

For the second hiker,

tan 21 = 525/y

=> y = 525/tan 21

let;

S = horizontal distance between the two hikers

=>S= x + y = 525/tan 37 + 525/tan 21

S = 525(1/tan 37 + 1/tan 21)

S = 2064 m

(D)