A flagpole stands on top of a building. From a point 25 metres away from the base of the building, the angle of elevation to the top of the flagpole is 60°, and to the top of the building is 30°. What is the height of the flagpole? (Round your answer off to the nearest metre, and use √3=1.7)
29 m
Let the building height be \(h_1\) and the total height (building + flagpole) be \(h_2\), with the observation point 25 m from the base.
\(h_1 = 25\tan30^\circ = \dfrac{25}{\sqrt3}\) and \(h_2 = 25\tan60^\circ = 25\sqrt3\).
Flagpole height: \(h_2-h_1 = 25\sqrt3-\dfrac{25}{\sqrt3} = 25\left(\sqrt3-\dfrac{1}{\sqrt3}\right) = 25\times\dfrac{2}{\sqrt3} = \dfrac{50}{\sqrt3}\).
Using \(\sqrt3=1.7\): \(\dfrac{50}{1.7} \approx 29.41\), which rounds to 29 m.
Hence, the height of the flagpole is approximately 29 m.
Similar Questions
- What is the distance of a vehicle from a tower of 150 m, if the angle of depression to the vehicle is $45^{\circ}$?
- The angle of elevation of a lamp post changes from $30^{\circ}$ to $60^{\circ}$ when a person walks 30 m towards it. Find the height of the lamp post.
- The angle of elevation of a ladder leaning against a wall is $45^\circ$. The foot of the ladder is $4\sqrt{2}$ metres away from wall. The length of the ladder is:
- From a watch tower of 200 m height, angles of depression of two cliffs in a horizontal line through the base of the tower are $45^{\circ}$ and $30^{\circ}$. Find the distance between the cliffs if they are on the same side.
- From a point Y on a level ground, the angle of elevation of the top of a lamp post is $45^\circ$. If the distance of point Y from the foot of the lamp post is 80 m, the height of the lamp post will be:
- A kite is flying with a thread of length 296 m, making an angle of elevation measuring 30° at a point of hand of a person of height 2m from the ground. Find the height of the kite from the ground.
- A tree broke at a height of 8 m from its foot and the broken upper part touches the ground at a point of 6 m from its foot. Find the height of the tree.
- An observer at the top of a tower observes that two cars are running towards the foot of the tower at a distance of 120 m from each other making angles of depression $\alpha$ and $\beta$ such that $\alpha > \beta$ and $\tan \alpha = \sqrt{3}$ and $\tan \beta = \frac{1}{\sqrt{3}}$. Find the height of the tower.
- Find the angle of elevation of a $200\sqrt{3}$ m tower's top from a point 200 m away from its base.
- Due to a cyclone, a tree is broken and makes an angle of $30^\circ$ with the ground. The distance between the root and the tip of the tree that touches the ground is 10 m. What is the height of the tree?
Important Questions from Heights and Distances
A peacock sitting at the top of a 3 meter high pole saw a snake approaching towards pole at a distance three times of the height of the pole. Then it jumping from pole will catch the snake at what distance from the pole if both are running with same speed ?
The foot of a ladder 25 m long is 7 m from the base of the building. If the top of the ladder slips by 4 m, then by how much distance will the foot of the ladder slide?
Two hotels stand 25 m apart. One of them is 70 m high and the angle of depression of the top of other as observed from the top of this hotel is 45°. Height of the other hotel is:
If the angles of elevation of a balloon from two consecutive kilometer-stones along a straight road are 30° and 60° respectively, then the height of the balloon above the ground will be:
The angle of elevation of the top of a tower from a point 20 m away from its base is 45 °. What is the height of the tower?
