Q. 1. The hypotenuse of right triangle is. If the smaller leg is tripled and the longer leg doubled, new hypotenuse will be 9Ö5 cm. How long are the legs of the triangle?
Q. 2. The shadow of a tower, standing on level ground is found to be 45 m longer when the Sun’s altitude is 300 than when it was at 600. Find the height of the tower. (Correct to 2 places of decimal).
Q. 3. The angle of elevation of an aeroplane from a point P on the ground is 60o. After a flight of 15 seconds. The angle of elevation changes to 300. If the aeroplane is flying at a constant height of 1500Ö3 m, find the speed of aeroplane.
Q. 4. From a point 20 m away from the foot of a tower, the angle of elevation of the top of a tower is 300. Find the height of the tower. (Correct to 2 places of decimal)
If 
, prove that 
Or
Evaluate:-
.
Q. 6. Prove that:-
Or
Prove that:- 
Q. 7. Prove that:- 
Or
Evaluate:- 
Q. 8. The angle of elevation of the top of a tower at the top of a building of height h is α and the angle of depression of the bottom of the tower at the top of the building is β. Prove that the height of the tower is
Or
A vertical tower has a flagstaff mounted over it. The height of the tower is h. The angles of elevation of the top and bottom of the flagstaff on the ground are α and β respectively. Prove that the height of the flagstaff is 
.
Q. 9. A man on a cliff observe a boat at an angle of depression of 300 which is approaching the shore to the point immediately beneath the observe with a uniform speed. Six minutes later the angle of depression of the boat is found to be 600. Find the time taken by the boat to reach the shore.
Or
A vertical tower stands on a horizontal plane and is surmounted by a vertical Flagstaff of height h. At a point on the plane, the angle of elevation of the bottom of the flagstaff is a and that of the top of flagstaff isb. Prove that the height of the tower is h tana/(tanb - tana).
