From the top of a 240-ft lighthouse, the angle - id2404664061, mooreadrian412

Ответ:

theojw

15.01.2022

The distance between ship and base of light house is 514.69 feet

Solution:

Given that, From the top of a 240-ft lighthouse, the angle of depression to a ship in the ocean is 25°

The figure for the problem is attached below

ABC is a right angled triangle

AB = height of light house = 240 feet

BC = distance between ship and base of light house

Angle of depression = 25 degrees

By using defintion of tan,

$tan \theta = \frac{opposite}{adjacent}$

In right angled triangle, ABC,

Opposite = AB and adjacent = BC

$tan\ 25 = \frac{240}{BC}\\\\0.4663 = \frac{240}{BC}\\\\BC = 514.69$

Thus distance between ship and base of light house is 514.69 feet

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