SOLUTION: Points A and B are on the same horizontal line with the foot of a hill and the angles of depression of these points from the top of the hill are 30.2° and 22.5°, respectively. I

Algebra.Com
Question 1198352: Points A and B are on the same horizontal line with the foot of a hill and the angles of depression of these points from the top of the hill are 30.2° and 22.5°,
respectively. If the distance between A and B is 75.0m, what is the height of the hill?
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

This is what the diagram would look like

Point C is the base of the hill, and D is the top of the hill.
Point E is to help set up the angles of depression (angle EDA = 22.5° in red; angle EDB = 30.2° in blue)

An angle of depression is where you start facing directly horizontal. Then you aim downward that amount of degrees to face the object.

Segments AC and ED are parallel as they are horizontal lines.
Using the alternate interior angle theorem, we have these two facts:This is an equivalent diagram where this time we're focusing on angles of elevation.

The reason why I'm doing this is to then bring your attention to these similar problems in the links below:
https://www.algebra.com/algebra/homework/Vectors/Vectors.faq.question.1198061.html
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1198040.html
In those links I've used angles of elevation, and the distance between observation points, to determine the height of the tall object.

This hint should be a good enough start to get you going.
If you're still stuck, then please let me know.
RELATED QUESTIONS

From the top of a hill 42.5 m above a stream, the angles of depression to a point on the... (answered by ikleyn,jim_thompson5910)
The angle of depression of a point on the 225m contour line is 10.2° from the top of a... (answered by ikleyn)
the angles of elevation of the top of a cliff from two boats A and B on the same side of... (answered by ikleyn)
The angle of depression of a point X on the ground from the top of a hill is 61°48.If the (answered by josgarithmetic)
From an observation tower that overlooks a runway, the angles of depression of Point A,... (answered by josgarithmetic)
1.A Boat is viewed From top of hill Which is 2000 Ft above sea and the angle is 30... (answered by josgarithmetic,MathTherapy)
From a balloon 3 km high, the angles of depression to two buildings in line and on the... (answered by Boreal)
Solve the following practical application. Provide a systematic solution with... (answered by josgarithmetic,ikleyn,math_tutor2020)
Two points in line with a tower and in the same horizontal plane with its base are 180... (answered by MathLover1)