Question

1) A ladder that is 15m long is leaning up against a building. The ladder makes an angle of 30 degrees with the ground.

a) Find an exact expression for the height at which the top of the ladder contacts the wall of the building.

2) A tree is anchored by a guy wire that is attached 13m from the base of the tree and makes an angle of 60 degrees with the ground. Find the exact values of the height of the tree.
- I know the answer for this question is 13√3 m, but I don't know how they got this.

Answer 1

Did you make a sketch?

1) sin30° = h/15
h = 15sin30
= 15(1/2)
= 7.5 m

Very unsafe way to place a ladder, the angle should be > 76° at the ground

2) in reference to the 60° angle, the 13 m is the "adjacent" and you want the "opposite" side
What trig ratio has those two words in it?

You should also know the ratio of sides of the
30-60-90° triangle is 1 : √3 : 2

since you want tan 60°, which is √3/1 or √3
that should explain where their answer comes from