Help with Angles of Elevation and Depression Please!!!?

Question

I need major help on these five problems. If you could show me how to do them and explain them I would greatly appreciate it!!! Oh, and I'll give Best Answer!!!

P.S. The * icon stands for degrees

1. The angle of elevation for a kite you are flying is 31*. If you have a 1000-ft roll of string and it is all out, how high is the kite? Assume that the string of the kite follows a linear path.

2. From a point 65 ft from the base of a telephone pole, the angle of elevation to a man working on the pole is 55*. The angle of elevation to the top of the pole is 70*. Find the distance from the man to the top of the pole.

3. A tree is 18 ft from a house. From the top of the tree, the angle of depression to the base of the house is 41*, and the angle of elevation to the top of the house is 26*. Find the height of the house.

4. A jet took off at a rate of 280 ft/s and climbed in a straight path for 4.5 min. What was the angle of elevation of its path if its final altitude was 16,500 ft?

5. The pilot of your tour helicopter has just announced that you are flying at an altitude of 1500 ft. If the launch pad where you are to land is 9000 ft away, at what angle of depression should you fly to reach the pad in the shortest time?

Answer 1

1. The formula for this equation is a simple Sine formula.

Sin = Opposite/hypotenuse

So in this case, (h will represent height)

Sin 31* = h/1000

Sin 31 x 1000 = h/1000 x 1000 (that will eliminate '1000' on this side)

1000 x Sin31 = 515.0380749... (use a calculator)

So the height is about 515 ft.

2. In the problem, you'd use Tangent.

Tan = opposite/adjacent

So... (h will symbolize the height of the pole)

Tan 55* = h/65

Tan 55 x 65 = h/65 x 65 (that will eliminate the '65' on this side)

65 x Tan55 = 92.82962044...

So the height is about 93 ft.

3. Here, we need to apply Tan to first find the height of the tree then again to find the height of house from the top of the tree.

So, (ht is the height of the tree)

Tan 41 = 18/ht

Tan 41 x ht = 18/ht x ht (the ht is now gone from this side)

Tan 41 x ht = 18

Now, divide both sides by Tan 41.

ht = 55.39830367...

Now for the rest of the house (H will represent the rest of the house)

Tan 26 = H/18

Tan 26 x 18 = H

H= 8.779186594...

To find out the total height of the house, add H and ht.

8.779186594... + 55.39830367...

So the house is about 64.18 ft.

4. Four and a half minutes is 270 seconds. So, if the plane is going 280 ft/s we can use ratio.

280             16500

------            ---------

  1                270

To find the angle of elevation we use Tan.

So (unknown angle is F)

Tan F = 16500/270

Now to move the 'Tan' to the other side. When 'Tan' crosses over it becomes 'Tan-1' (look on your calculator)

F= tan-1 16500/270

F= 89.06251637...

The angle is about 89*

5. i'm not quite sure about what kind of situation this question is. there are two options. could you be more specific?