# physics

posted by .

A lighthouse standing on the top of a cliff is observed from two open boats (boats are not decked over) A and B in a vertical plane through the light house. The angle of elevation of the top of the lighthouse viewed from B is 16 degrees and the angles of elevation of the top and bottom viewed from A are 40 degrees and 23 degrees respectively. If the boats are 1320 ft. apart, find the height of the lighthouse and the height of the cliff.

• physics -

c = cliff height
h = lighthouse hight
a = distance of A from cliff
b = distance of B from cliff

c/a = tan 23°
(c+h)/a = tan 40°
(c+h)/b = tan 17°

So, clearing fractions and plugging in the trig values, we have

c = .4245a
c+h = .8391a
c+h = .3057b
b = a+1320

h = 313.65
c = 321.14

## Similar Questions

1. ### formal geomerty

A person in a small boat sights the top of a 40-foot lighthouse found on a cliff. The angle of elevation to the top of the lighthouse is 50.2 degrees. If the distance from the base of the cliff to the boat is 75 feet,what is the height …
2. ### Precalculus

1. A man stands 12 feet from a statue. The angle of elevation from the eye level to the top of the statue is 30 degrees, and the angle of depression to the base of the statue is 15. How tall in the statue?
3. ### trigonometry

A lighthouse BC of unknown height stands on the edge of a cliff AB. From a point O, 2500 ft from the base of the cliff, an observer measures the angles of elevation of the top and bottom of the lighthouse and finds them to be 15°40' …
4. ### trig

A plane is flying 12,000 feet horizontally from a tall, vertical cliff. The angle of elevation from the plane to the top of the cliff is 45degrees, while the angle of depression from the plane to a point on the cliff at elevation 8000 …
5. ### maths

From the top of a cliff 150m high, the angles of depression of two boats are 60 and 30. Find the distance between the boats if they are on the opposite sides of the cliff.
6. ### maths-urgently needed

From the top of a cliff 150m high, the angles of depression of two boats are 60 and 30. Find the distance between the boats if they are on the opposite sides of the cliff.
7. ### math

A person in a lighthouse notices two boats out on the ocean. The angle of depression to the further boat is 20 degrees while the angle of depression to the closer boat is 75 degrees. What is the distance between the two boats if the …
8. ### Math

Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 degrees and 45 degrees respectively. If the lighthouse is 100m high, the distance …
9. ### Geometry

There is a flagpole in the school parking lot. Which of the following is true about the angle of depression from the top of the flagpole to the parking lot, and the angle of elevation from the parking lot to the top of the flagpole?
10. ### core mathematics

Two boats are 70m and on opposite sides of a lighthouse.from the two boats,the angles of elevation of the lighthouse are 71 and 45 respectively.find the height of the lighthouse.

More Similar Questions