English

Find the Length of the Shadow Cast by a Tree 60 M High When the Sun'S Altitude is 30 ∘ . - Mathematics

Advertisements
Advertisements

Question

Find the length of the shadow cast by a tree 60 m high when the sun's altitude is `30^circ`.

Sum

Solution

Let AB be the tree of height 60 m and BC be its shadow .

In ΔABC

`"AB"/"BC"` = `tan30^circ`

`60/"BC" = 1/sqrt(3)`

`"BC" = 60sqrt(3)` m

So , height of tower is `60sqrt(3)` m .

shaalaa.com
Heights and Distances - Solving 2-D Problems Involving Angles of Elevation and Depression Using Trigonometric Tables
  Is there an error in this question or solution?
Chapter 22: Heights and Distances - Exercise

APPEARS IN

Frank Mathematics - Part 2 [English] Class 10 ICSE
Chapter 22 Heights and Distances
Exercise | Q 5

RELATED QUESTIONS

An aeroplane at an altitude of 250 m observes the angle of depression of two boats on the opposite banks of a river to be 45° and 60° respectively. Find the width of the river. Write the answer correct to the nearest whole number.


The angle of elevation of the top of a tower, from a point on the ground and at a distance of 160 m from its foot, is found to be 60°. Find the height of the tower.


At a particular time, when the sun’s altitude is 30°, the length of the shadow of a vertical tower is 45 m. Calculate:

  1. the height of the tower.
  2. the length of the shadow of the same tower, when the sun’s altitude is:
  1. 45°
  2. 60°

From the top of a cliff 92 m high, the angle of depression of a buoy is 20°. Calculate, to the nearest metre, the distance of the buoy from the foot of the cliff.


At a point on level ground, the angle of elevation of a vertical tower is found to be such that its tangent is `5/12`. On walking 192 metres towards the tower, the tangent of the angle is found to be `3/4`. Find the height of the tower.


The angles of elevation of the top of a tower from two points on the ground at distances a and b metres from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is `sqrt(ab)` metre.


The distance of the gate of a temple from its base is `sqrt(3)` times it height. Find the angle of elevation of the top of the temple.


The top of a ladder reaches a pcint on the wall 5 m above the ground. If the foot of the ladder makes an angle of 30° with the ground, find the length of the ladder. 


A ladder rests against a wall at an angle a, to the horizontal. Its foot is pulled away from the wall through a distance 'a', so that it slides a distance 'b' down the wall making an angle β with the horizontal. Show that `"a"/"b" = (cosα - cosβ)/(sinβ - sinα).` 


A man on the top of vertical observation tower observes a car moving at a uniform speed coming directly towards it. If it takes 12 minutes for the angle of depression to change from 30° to 45°, how soon after this will the car reach the observation tower? (Give your answer correct to nearest seconds).


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×