Can you tell me if these answer is correct.

Question

1. From a boat on the lake, the angle of elevation to the top of a cliff is 35degrees13'. if the base of the cliff is 2664 feet from the boat, how high is the cliff(to the nearest foot)?
i got 1880 feet. is this correct.
and this one:
From a ballon 996 feet high, the angle of depression to the ranger headquarters is 46deg49'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?
I think its 930 feet. am i right?

Answer 1

first one is correct

for the second the angle of depression is measured down from a horizontal, so the angle of elevation from the station to the balloon is the same or 46.816666º

so tan 46.816666 = 996/x
x = 996/tan46.816666
= 934.8

Answer 2

thanks alot. i really like ur way of explaining.

Answer 3

From a boat on the lake, the angle of elevation to the top of a cliff is 27°57'. If the base of the cliff is 128 feet from the boat, how high is the cliff (to the nearest foot)?

Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 23°29'. Find the height of the mountain to the nearest foot if Bob is 16,194.6 feet from the center of the mountain at the base.

Answer 4

From a boat on the lake, the angle of elevation to the top of a cliff is 27°57'. If the base of the cliff is 128 feet from the boat, how high is the cliff (to the nearest foot)?