SELF TEST:
Q1. A person, standing on the bank of a river, observes that the angle subtended by a tree on the opposite bank is 60°. When he retreated 20m from the bank, he finds the angle to be 30°. Find the height of the tree and the breadth of the river. ( 3 mk)
Q 2. A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance of 30 meters from the roots. Find the whole height of the tree. ( 3 mk)
Q3. At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is 5/12 . On walking 192 meters towards the tower, the tangent of the angle of elevation is 3/4. Find the height of the tower. ( 3 mk)
Q4. A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60o. When he moves 40 meters away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and the width of the river. ( 3 mk)
Q5. A man on the top of a vertical tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the tower? Give your answer to the nearest second. ( 3 mk)
Q6.The shadow of a flag – staff is three times as long as the shadow of the flag – staff when the sun rays meet the ground at an angle of 60°. Find the angle between the sun rays and the ground at the time of longer shadow. ( 3 mk)
Q7. An aeroplane at an altitude of 200m observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river. ( 2 mk )