1. A kite is flying with the string inclined at an angle of 42° to the horizontal. Find the height of the kite above the ground when the string is 50metres long and attached to a peg in the ground.

2. A flagstaff, 21metres high, standing on horizontal ground is held up by ropes. Each rope being attached to the top of the flagstaff and to a peg in the ground and inclined at 30° to the vertical. Find the lengths of the ropes and the distance of the pegs from the foot of the flagstaff.

3. To find the height of a tower a surveyor sets up his theodolite some distance from the foot of the tower and finds the angle of elevation to the top of the tower to be 30°. He then moves 60metres nearer to the tower and finds the angle of elevation to be 42°. Find the height of the tower assuming the ground is horizontal and that the instrument is 1.5 metres above ground level.

4. From a window 8.2 metres above the street the angle of depression of the base of the house across the street is 35.5° and the angle of elevation of its rooftop is 12.5°. Find the width of the street and the height of the house across the street.