SOLUTION: At point "A" due east to a hut, the angle of elevation is 55° and at point "B" due it's west the angle of elevation is 45°. The distance from point A to B is 15m. Find height of

Question 1196263: At point "A" due east to a hut, the angle of elevation is 55° and at point "B" due it's west the angle of elevation is 45°. The distance from point A to B is 15m. Find height of the hut?
Found 3 solutions by josgarithmetic, math_tutor2020, amoresroy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Draw the described situation.
T, point at tip of the hut.
Understand, a point is directly under T and is on segment BA.
Triangle BTA;
Interior angle at B is 45 degrees and interior angle at A is 55 degrees.
x, the length from B to the point on the segment, underneath T.
15-x, the length from A to the point on the segment, underneath T.

How high the tip of the the hunt, y.

Check the triangle part with the 45 elevation angle. That part is special 45-45-90 triangle. this mean, .

Just solving the second equation,

Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

This is one way to draw out the diagram

Let x be the length of segment AD
And let y be the height of the hut (i.e. the length of segment CD)

Triangle BCD is a 45-45-90 triangle
The two legs (BD and CD) are the same length
So BD = y and CD = y

AB = 15
AD = x
BD = AB - AD
BD = 15 - x

Since BD = y was mentioned earlier, and BD = 15-x, we can say y = 15-x

For triangle ACD, we can say:
tan(angle) = opposite/adjacent
tan(A) = CD/AD
tan(55) = y/x
x*tan(55) = y
y = x*tan(55)

Now plug in y = 15-x and solve for x
y = x*tan(55)
15-x = x*tan(55)
15 = x*tan(55)+x
x*tan(55)+x = 15
x*(tan(55)+1) = 15
x = 15/(tan(55)+1)
x = 6.17754764468651

Then use this to find the value of y
y = 15-x
y = 15-6.17754764468651
y = 8.8224523553135
y = 8.822452
Or,
y = x*tan(55)
y = 6.17754764468651*tan(55)
y = 8.82245235531349
y = 8.822452

Answer: Approximately 8.822452 meters

Similar question:
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1196262.html

Answer by amoresroy(361)   (Show Source): You can put this solution on YOUR website!
Let h = height of the hut
Expressing given problem to systems of equations
(1) Tan 55 = h/(15-x) = 1.428
(2) Tan 45 = h/x = 1
x = h
Substitute x = h in equation (1)
h/(15-h) = 1.428
h = 1.428(15-h)
h = 21.422 - 1.428h
2.428h = 21.422
h = 8.823
Answer
The height of the hut is 8.823 meters.

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