Advertisements
Advertisements
Question
A storm broke a tree and the treetop rested 20 m from the base of the tree, making an angle of 60° with the horizontal. Find the height of the tree.
Solution
Let AC be the original height of the tree. Suppose BD be the broken part of the tree which is rested at D from the base of the tree.
Here, CD = 20 m and ∠BDC = 60º.
In right ∆BCD,
\[\tan60^\circ = \frac{BC}{CD}\]
\[ \Rightarrow \sqrt{3} = \frac{BC}{20}\]
\[ \Rightarrow BC = 20\sqrt{3} m . . . . . \left( 1 \right)\]
Also,
\[\cos60^\circ = \frac{CD}{BD}\]
\[ \Rightarrow \frac{1}{2} = \frac{20}{BD}\]
\[ \Rightarrow BD = 40 m . . . . . \left( 2 \right)\]
∴ Height of the tree = AB + BC = BD + BC =
\[\left( 40 + 20\sqrt{3} \right) m\] [Using (1) and (2)]
Thus, the height of the tree is \[\left( 40 + 20\sqrt{3} \right) m\]
APPEARS IN
RELATED QUESTIONS
A balloon is connected to a meteorological station by a cable of length 200 m, inclined at 60º to the horizontal. Find the height of the balloon from the ground. Assume that there is no slack in the cable
The heights of two poles are 80 m and 62.5 m. If the line joining their tops makes an angle of 45º with the horizontal, then find the distance between the pole
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30°. Find the distance travelled by the balloon during the interval.
A balloon is connected to a meteorological ground station by a cable of length 215 m inclined at 600 to the horizontal. Determine the height of the balloon from the ground. Assume that there is no slack in the cable.
From a point on the ground 40m away from the foot of a tower, the angle of elevation of the top of the tower is 30 . The angle of elevation of the top of a water tank (on the top of the tower) is 45 , Find (i) the height of the tower, (ii) the depth of the tank.
The angle of elevation of the top of a vertical tower from a point on the ground is 60° . From another point 10 m vertically above the first, its angle of elevation is 30° .Find the height of the tower.
A storm broke a tree and the tree top rested on ground 20 m away from the
base of the tree, making an angle of 60o with the ground. Find the height
of the tree.
What is the angle of elevation of the Sun when the length of the shadow of a vetical pole is equal to its height?
If the altitude of the sum is at 60°, then the height of the vertical tower that will cast a shadow of length 30 m is
Two poles are 'a' metres apart and the height of one is double of the other. If from the middle point of the line joining their feet an observer finds the angular elevations of their tops to be complementary, then the height of the smaller is
A tree is broken by the wind. The top struck the ground at an angle of 30° and at a distance 30 m from the root. Find the whole height of the tree. (`sqrt(3)`=1.73)
A building and a statue are in opposite side of a street from each other 35 m apart. From a point on the roof of building the angle of elevation of the top of statue is 24° and the angle of depression of base of the statue is 34°. Find the height of the statue. (tan 24° = 0.4452, tan 34° = 0.6745)
A Technician has to repair light on a pole of height 10 m. She needs to reach a point 1 m below the top of the pole to undertake the repair work. What should be the length of the ladder that she should use which, when inclined at an angle of 60∘ to the ground, would enable her to reach the required position? Also, how far from the foot of the pole should she place the foot of the ladder?
A contractor plans to install two slides for the children to play in a park. For the children below the age of 5 years, she prefers to have a slide whose top is at a height of 2m and is inclined at an angle of 30° to the ground. What should be the length of the slide?
A kite is flying at a height of 30 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming that there is no slack in the string.
If a man standing on a platform 3 meters above the surface of a lake observes a cloud and its reflection in the lake, then calculate the angle of elevation of the cloud.
A ladder 15 meters long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall will be ____________.
The shadow of a tower standing on a level plane is found to be 50 m longer when Sun’s elevation is 30° than when it is 60°. Find the height of the tower.
Lakshaman Jhula is located 5 kilometers north-east of the city of Rishikesh in the Indian state of Uttarakhand. The bridge connects the villages of Tapovan to Jonk. Tapovan is in Tehri Garhwal district, on the west bank of the river, while Jonk is in Pauri Garhwal district, on the east bank. Lakshman Jhula is a pedestrian bridge also used by motorbikes. It is a landmark of Rishikesh. A group of Class X students visited Rishikesh in Uttarakhand on a trip. They observed from a point (P) on a river bridge that the angles of depression of opposite banks of the river are 60° and 30° respectively. The height of the bridge is about 18 meters from the river. |
Based on the above information answer the following questions.
- Find the distance PA.
- Find the distance PB
- Find the width AB of the river.
[OR]
Find the height BQ if the angle of the elevation from P to Q be 30°.
Two pillars of equal lengths stand on either side of a road which is 100 m wide, exactly opposite to each other. At a point on the road between the pillars, the angles of elevation of the tops of the pillars are 60° and 30°. Find the length of each pillar and the distance of the point on the road from the pillars. (Use `sqrt3` = 1.732)
