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Margaret [11]
3 years ago
11

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 pe

rson 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

Mathematics
1 answer:
8090 [49]3 years ago
3 0

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 tan 65 = \frac{h}{45-x} = 2.14

h=2.14(45-x)

From ΔBCO tan80 = \frac{h}{x} = 5.67

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 cos80 = \frac{x}{OB}

0.174 = \frac{12.33}{OB}

OB = \frac{12.33}{.174}=70.86=71ft.

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

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