Question about depression angles and Trig

[LoganPops]

Hi, I've been having trouble with my trig work, I understand all of the regular questions but the depression angles got me tripped up I don't understand what to do with them. Thanks.

Homework question exactly: A helicopter is flying over Ottawa and sees the tower on Parliament hill and a tree straight across the river in Gatineau. The pilot determines the angle of depression to both the tree and the tower and knows how wide the river is at that point (and, therefore, the distance between the tree and the tower).
Determine the distance from the helicopter to the tree, and the distance from the helicopter to the tower.
Homework Picture Exactly with values that I picked:

 

[Dr.Peterson]

Angles of depression are always acute angles, so your B is a little odd ... . And if the tower is on the hill and the tree is lower, that makes the problem a little harder than the picture shows. But I'll go by the picture.

A key idea here is that the base angles of the triangle are congruent to the angles of depression (being alternate interior angles), so they, too, are respectively A and B.

Now, do you want to solve this using the Law of Sines, or by dropping a vertical line from the helicopter and working with the two right triangles? The former is probably easier.

Please show your thoughts, so we can know what help you need.

 

[LoganPops]

Angles of depression are always acute angles, so your B is a little odd ... . And if the tower is on the hill and the tree is lower, that makes the problem a little harder than the picture shows. But I'll go by the picture.

A key idea here is that the base angles of the triangle are congruent to the angles of depression (being alternate interior angles), so they, too, are respectively A and B.

Now, do you want to solve this using the Law of Sines, or by dropping a vertical line from the helicopter and working with the two right triangles? The former is probably easier.

Please show your thoughts, so we can know what help you need.

Law of sines is what I need to solve it with for the assignment. I changed the value of B to 56 to make it make more sense. Thank you for pointing that out to me.

Since you told me angles A and B are congruent to the base I think I can figure it out.

Thank you.