Question

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?

Answer 1

71.10 feet

Explanation:

To solve this you have to remember the laws of the triangles and the law of sines, this states that every triangle´s sum of the inner angles are 180º

This means that if angle A is 65º and angle B is 80º angle C which would be the angle created on the top oof the mountain byt the lines that conect the top of the mountain with person A and B would be 35º.

Now the law of sines goes like this:

`(A)/(Sine angle A)=(B)/(Sine angle B)=(C)/(Sine angle C)`

If you put the values of the different angles you´d get:

`(x)/(sine 65)=(45)/(sine 35)`

When you clear the equation it will end up like this:

x=
`((sine 65)(45))/(sine 35)`

x= 71.1

Answer 2

see the picture to better understand the problem

we know that
in the triangle ABC
∠A+∠B+∠C=180°
find ∠C
∠C=180-[80+65]------> ∠C=35°

Applying the law of sines

AB/sin C=CB/sin A
solve for CB
CB=AB*sin A/sin C-----> CB=45*sin 65/sin 35-----> CB=71.10 ft

the answer is
the distance from person B to the top of the hill is 71.10 feet