Math Problem Solver

1) From the top of a rock of 100 m. high ,the depression angles of the top and the base of a

tower were measured to be 22° ,33° respectively. Find the height of the tower to the nearest

meter given that the base of the rock and the base of the tower are in the same horizontal

plane.

2) A light. house of height 60 meters is constructed in a hill near sea short the elevation angles

of the top and the base of the light house were measured from a boot on the sea level and

found to be 70° and 45° respectively find the height of the hill ( above the sea level) to nearest

meter.

3) From a helicopter at a height 200 m above the sea level two ships are observed the measure

of their depression angle were 24°, 37° respectively if the vertical projection of the plan on

the sea level lies on the straight line joining the two ships and between them find the distance

between the two ships

4) A car travels along a straight road, heading west for three hours, and then travels

northeast on another road for two hours. If the car has maintained a constant speed of 55

km/h, how far is it from its starting position?

5) From the top of a house of 6 m. high, the measure of the angle of elevation of the top of a

tree was 20° and the measure of the angle of depression of the base of the tree was 300 Find

the distance between the base of the house and the base of the tree, find also the height of

the tree given that the two bases are in the same horizontal plane.

6) A girl is flying two kites at the same time. If the strings are 70 meters and 80 meters long

and the kites are 32 meters apart, what angle do the strings make in her hands?

7) A tower 42 meter high, stands on top of a hill. From a point some distance from the base

of the hill, the angle of elevation to the top of the tower is 13° From the same point the

angle of elevation to the bottom of the tower is 8°. Find the height of the hill.