Chapter 13

Height and Distance

1. Determine the height of a mountain if the elevation if the elevation of its top at an unknown distance from the base is 45⁰ and at a distance 10km further off from the mountain, along the same line, the angle of elevation is 30⁰ (USE tan30⁰ = 0.5774).
    
2. The angle of elevation of the top of a rock from the top and foot of a 100m high tower are respectively 30⁰ and 45⁰. Find the height of the rock.
    
3. The angle of elevation of the top Q of a vertical tower PQ from a point X on the ground is 60⁰. At a point Y, 40m vertically above X, the angle of elevation is 45⁰. Find the height of the tower PQ and the distance XQ.
    
4. An aeroplane, when 3000m high, pass vertically above another aeroplane at an instance when the angles of elevation of the two aeroplanes from the same point on the ground are 60⁰ and 45⁰ respectively. Find the vertical distance between the two aeroplans.
    
5. A pole 5m high is fixed on the top of a tower. The angle of elevation of the top of the pole observed from a point A on the ground is 60⁰ and the angle of depression of the point ‘A’ from the top of the tower is 45⁰. Find the height of the tower.
    
6. A tower is 50m high. Its shadow is x m shorter when the sun’s altitude is 45⁰ than when it is 30⁰. Find x. .....................