Trigonometry Questions

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

1)

x = distance of ship from lighthouse

angle of elevation to top of lighthouse is 24 degrees

tan 24 = x/229

x = 229 * tan 24 = 101.96 feet

2)

x = height of cloud cover

tan 43 = x/553

x = tan 43 * 553 = 515.68 m

3)

x1 = height of tower from ground to top of building

x2 = height of tower starting from top of building

x1 + x2 = total height of tower

tan 37 = x1/375

x1 = 375 * tan(37) = 282.58

tan 42 = x2/375

x2 = 375 * tan(42) = 337.65

height of tower = 282.58 + 337.65 = 620.23 feet