Trigonometry Question

Question

1. From the top of a 229-ft lighthouse, the angle of depression to a ship in the ocean is 24 degrees How far is the ship from the base of the lighthouse?
2. To measure the height of the cloud cover at an airporta worker shines a spotlight upward at an angle of from the horizontal. An observer 553 m away measures the angle of elevation to the spot of light to be 42 degrees °. Find the height of the cloud cover. height = Report answer accurate to 2 decimal places.
3. A radio tower is located 375 feet from a buildingFrom window in the building a person determines that the angle of elevation to the top of the tower is 42 degrees and that the angle of depression to the bottom of the tower is 37 degrees tall is the tower? In Feet

Answer 1

I strongly suggest to sketch or draw a triangle with the information of problem 1. My labeling is below.

Let construct a triangle with the data from the problem. The observer is at point T (top of the tower), The base of the tower would be B, and the ship would be at point S.

Triangle TBS is right triangle, because the tower is perpendicular to the sea level. We know the length of the side TB = 229 feet. The angle at which we see TB from point S is 24^o. We are looking for the side SB, the distance from the ship to the base of the tower.

The ratio TB:SB = tan(24^o). We write this as an equation:

229/x = 0.445

x = 229/0.445,

x = 514.34 feet.

In similar manner you can solve the other two problems.

First, you draw a sketch to familiarize with the problem. Find the right triangle that has the given information and decide which ratio, sine, cosine or tangent is appropriate. Write your equation and solve.

If you still need help, let me know.

Part 2: height = 497.92 feet.

Part 3: tower_height = 620.23.

Hint: draw horizontal line from building to the tower. Extra: imagine you are in the building. You can see on which floor you are to make such observation (one floor = 10 feet).