Solve each of the following problems with Solution

Question

1) A flagpole is situated at the top of a building 115 ft tall. From a point in the same horizontal plane as the base of the building the angles of elevation of the top and bottom of the flagpole are 63.2 ° and 58.6 ° , respectively. How tall is the flagpole?

2) A ramp is inclined at an angle of 41.3° with the ground. One end of a board, 20.6 ft in length, is located on the ground at a point P, 12.2 ft from the base Q of the ramp, and the other end rests on the ramp at point R. Find the distance from point Q up the ramp to point R.

3) A ship is sailing due north. At a certain point, the captain of the ship notices a lighthouse 12.5 km away from the ship, at the bearing of N 38.0° E. Later on, the bearing of the lighthouse becomes S 44.2° E. In meters, how far did the ship travel between the two observations of the lighthouse?

Answer 1

I used to give my geometry students problems like this!

We'd go out and "measure" real things around the school in this way.

I worked it out, and got that the flag pole was just under 24 feet high.

If you need to see the details of how I got that, let me know.

Answer 2

1)

Draw and label a diagram.

p represents the height of the pole

d represents the distance from the bulding to the observatio point

tan 58.6 = 115 / d

tan 63.2 = (115 + p) / d

Isoltate d in both, set equations equal, and solve for p

2)

Where is R located?

3)

Label all angles.

Use Law of Sines to determine distance.