A surveyor was unable to directly measure the height of the mountain, so he set up his equipment at the base o

Question

A surveyor was unable to directly measure the height of the mountain, so he set up his equipment at the base of the mountain at two different locations, A and B, 1500 meters apart from each other. He then measured the angle of elevation to the top of the mountain from each of these locations. The angle of elevation from point A is 20 degrees. The angle of elevation from point B is 32 degrees. Find the height of the mountain to the nearest meter.

Answer 1

Use triangulation

make a scale for this 1cm=30m

draw a baseline for this will be 5cm(=1500m)

draw your angels

connect the angels

draw a line from where they connect to the baseline and measure that

Answer 2

Draw a triangle with a base of 1500M and the to angles we know of 20 degrees and 32 degrees. The height of the triangle is the height of the mountain. Now draw a line perpendicular to the base that bisects the angle at the top of the triangle. This leaves you with 2 right triangles both with a leg equal to the height. we will call this h. the base is cut into 2 segments, we will call one segment x and the other 1500-x.



rec had the right idea but then changed the angles which he was using in each equation and made a math error.

But if you start off with the same base equation

h = x tan 20
h = (1500 - x) tan 32


so
xtan20=(1500-x)tan32
xtan20/tan32=1500-x
x+xtan20/tan32=1500
x(1+tan20/tan32)=1500
x=1500/(1+tan20/tan32)
x=947.883m

h=947.883m(tan20)=345.001m

Answer 3

draw the triangle and you'll see that the altitude of the triangle is the height of the mountain.

let h be the height of the mountain.

the base is intersected by the height. let's call x is one part of the segment and 1500 - x is the other part.

tan 32 = h / x
tan 20 = h / (1500 - x)

h = x tan 20
h = (1500 - x) tan 32

x tan20 = (1500 - x) tan 32
x tan20 = 1500 tan 32 - x tan 32
x tan 20 + x tan 32 = 1500 tan 32
x (tan 32 + tan 20) = 1500 tan 32
x =1500 tan 32 / (tan 20 + tan 32)
x = 342.1

h = 342.1 tan 20
h = 765.33 m ==> answer

Answer 4

Let

x - height of the mountain
y - horizontal distance of the point B from the mountain

then

x = (y+1500) * tang 20 degree
x = y * tang 32 degree

Now it's easy.

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Answer 5

Huh. Zero answers, 76 points. Sounds like someone is here just to get their summer school homework done for them.

I know the answer... but I ain't tellin'.