The angle of depression from the top of a flag stick to a golf ball on the ground is 24 degrees. If the flagstick is 6 feet tall, how far away is the golf ball from the base of the flag stick

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter5: Similar Triangles
Section5.5: Special Right Triangles
Problem 25E: A jogger runs along two sides of an open rectangular lot. If the first side of the lot is 200 ft...
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The angle of depression from the top of a flag stick to a golf ball on the ground is 24 degrees. If the flagstick is 6 feet tall, how far away is the golf ball from the base of the flag stick. 

Expert Solution
Step 1

Consider that the angle of depression from top of a flag stick to golf ball is 24° and length of flagstick is 6 feet.

Find the horizontal distance between the golf ball and flagstick.

 

Plot the diagram.

Algebra homework question answer, step 1, image 1

 

Let AB be the height of the flagstick and BC=x be the distance of golf ball from the base of the flag stick.

Since angle of depression is the angle between the horizontal line of sight and the object therefore, HAC is the angle of depression.

 

Since horizontal line of sight AH and base BC are parallel and AC is transveral,HAC and ACB form alternate angles and alternate angles are equal in measure therefore, HAC=ACB=24°.

 

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