Question

A person sights a boat from 235 feet above sea-level as shown. If the angle of depression from the man to the boat is 21 , then determine the boat's distance to the edge of the cliff to the nearest ten feet.

Answer 1

The distance of the boat from the edge of the cliff is 655.75 ft

Distance of the boat from the base of the cliff is 251.72 ft

Explanation:

Height of person above sea level = 235 ft

Angle of depression of sight to the boat from the person = 21°

Therefore, based on similar angle between person and angle of depression and the boat with angle of elevation we have,

Angle of elevation of the location of the person as sighted from the boat θ = 21°

Distance from the edge of the cliff of the boat is then given by;

`Sin\theta = (Opposite \, side \, to\, angle)/(Hypothenus\, side \, of\, triangle) = (Height\, of\, person\, above \, ses \, level)/(Distance\, of\, boat\, from \, edge\, of \, cliff)`

`Sin21 =(235)/(Distance\, of\, boat\, from \, edge\, of \, cliff)`

`Distance\, of\, boat\, from \, edge\, of \, cliff=(235)/(Sin21 ) = (235)/(0.358) = 655.75 \, ft`

Distance of the boat from the base of the cliff is given by

`Distance\, of\, boat\, from \, base\, of \, cliff=(235)/(cos21 ) = (235)/(0.934) = 251.72 \, ft`.

Answer 2

B = 612.2 ft

Explanation:

Solution:-

- The elevation of person, H = 235 ft

- The angle of depression, θ = 21°

- We will sketch a right angle triangle with Height (H), and Base (B) : the boat's distance to the edge of the cliff and the angle (θ) between B and the direct line of sight distance.

- We will use trigonometric ratios to determine the distance between boat and the edge of the cliff, using tangent function.

tan ( θ ) = H / B

B = H / tan ( θ )

B = 235 / tan ( 21 )

B = 612.2 ft