Question
From the top of a lighthouse, the angle of depression to the top and bottom of a tower is 30° and 45°, respectively. If the lighthouse is 210 metres high, then find the height of the tower.
Let AB and CD be the heights of the light house and the tower, respectively So, AB = 210 metres, ∠ ADE = 30° and ∠ ACB = 45° Now, in right angled triangle ABC tan45° = AB/BC So, AB/BC = 1 Or, AB = BC So, BC = 210 metres And, BC = DE = 210 metres So, in right angled triangle AED, tan30° = AE/DE Or, AE = 210 × (1/√3) Or, AE = 70√3 Also, CD = BE So, height of tower CD = AB – AE = 210 – 70√3 = 70√3(√3 – 1) metresMore Height and Distance Questions
- Two ships are on opposite sides in front of a lighthouse in such a way that all three of them are in line. The angles of depression of two ships from the t...
- The angle of elevation of the top of a building from a point on the ground is 30° and moving 40 meters towards the building it becomes 60°. The height of t...
- The angle of depression of a point on the ground as seen from the top of a tower, 20 feet high, is 45°. Find the distance of the point on the ground from t...
- There is a fire in the building. A man on the top of the building see a Fire brigade van coming towards it. If it takes 8 minutes for the angle of depressi...
- From the top of a straight pillar 20 meters high, the angle of elevation of the top of a straight tower was 45°. If the tower was 70 meters high, then at w...
- The angle of elevation of an aeroplane from a point on the ground is 60°. After 12 seconds flight the elevation changes to 30°, if the aeroplane is...
- There are two houses of the same height on both sides of a 15-meter wide road. From a point on the road, elevation angles of the houses are 30° and 60° res...
- A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 15 metres . From the top of the pole the angle of elevati...
- The angle of elevation of the top of a building from the foot of a tower is 30° and the angle of elevation of the top of the tower from the foot of the bui...
- A boat is being rowed away from a cliff 270 m high. From the top of the cliff, the angle of depression of the boat changes from 60° to 45° in 2 minutes. Wh...
Relevant for Exams:
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
