SOLUTION: At point "A" due east to a hut, the angle of elevation is 45° and at point "B" due it's west the angle of elevation is 30°. The distance from point A to B is 10m. Find height of

Question 1196262: At point "A" due east to a hut, the angle of elevation is 45° and at point "B" due it's west the angle of elevation is 30°. The distance from point A to B is 10m. Find height of the hut?
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

This is one way to draw out the diagram

Segment CD represents the height of the hut
Let's call it x for now.

Triangle ACD is a 45-45-90 triangle, aka an isosceles right triangle.
These types of right triangles have congruent legs.
We have CD = x and AD = x as those legs.

AB = 10
DB = AB - AD
DB = 10 - x

Triangle BCD is a 30-60-90 triangle, which means the long leg is exactly times that of the short leg.
Note the short leg of these types of triangles is always opposite the 30 degree angle. The smallest side is opposite the smallest angle.

So,

which is one way to express the exact height.
Another way is to rationalize the denominator.

Use a calculator to find that approximately

Answer: The height is roughly 3.66025 meters

Similar question:
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1196263.html

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