CBSE Class 10-Mathematics: Chapter – 9 Some Applications of Trigonometry Part 9 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Question 13:

The angle of elevation of the top of a tower at a point on the level ground is . After walking a distance of towards the foot of the tower along the horizontal line through the foot of the tower on the same level ground the angle of elevation to the top of the tower is , find the height of the tower.

The Angle of Elevation of the Top of a Tower

Answer:

In

In

Question 14:

As observed from the top of light house high above sea level the angle of depression of a ship sailing directly towards it changes from to . Determine the distance travelled by the ship during the period of observation.

Let PQ be the Light House

Answer:

Let be the light house such that . Let A and B be the positions of ship when the angle of depression changes from to respectively.

Let

From right-angled ,

From right-angled triangle BPQ,

From (i) and (ii) ,

Question 15:

The angles of elevation of the top of a tower from two points P and Q at distances of a and b respectively from the base and in the same straight line with are complementary. Prove that the height of the tower is where .

The Angles of Elevation of the Top of a Tower

Answer:

Let AB be tower of height h. Let P and Q be the given points in the same straight line with the foot B of the tower.

Let

From right angled

From right-angled

Multiplying (i) and (ii) , we get

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