Two people are standing on opposite sides of a hill. Person A makes an angle of elevation of 65° with the top of the hill and person B makes an angle of elevation of 80° with the top of the hill. The two people are standing 45 feet from each other. What is the distance from person B to the top of the hill? 29 ft 49 ft 71 ft 77 ft

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eudora eudora · Answer 1 · 2019-02-15T21:15:31+01:00

Answer:

Option 3. 71 ft. is the distance between B and top of the hill.

Step-by-step explanation:

Let the height of the hill is h ft and the distance of A from the hill be x ft and distance from B to hill is y.

It is given distance between A and B is 45 ft. ∠BAO = 65° and ∠ABO = 80°.

We have to find the distance of B from the top of the hill.

Now from ΔACO [tex]tan 65 = \frac{h}{45-x} = 2.14[/tex]

[tex]h=2.14(45-x)[/tex]

From ΔBCO [tex]tan80 = \frac{h}{x} = 5.67[/tex]

h = 5.67x

Now h = 5.67x = 2.14(45-x)

5.67x = 96.3 - 2.14x

2.14x + 5.67x = 96.3

7.81x = 96.3

x = 96.3/7.81 = 12.33 ft

Therefore [tex]cos80 = \frac{x}{OB}[/tex]

[tex]0.174 = \frac{12.33}{OB}[/tex]

[tex]OB = \frac{12.33}{.174}=70.86=71ft.[/tex]

Therefore 71 ft is the distance between B and the top of the hill.