+91-8076753736[email protected]
logo
logo
-->

Circles

Question
CBSEENMA10008349
Wired Faculty App

A man on the deck of a ship 14 m above water level, observes that the angle of elevation of the top of a cliff is 60° and the angle of depression of the base of the cliff is 30°. Calculate the distance of the cliff from the ship and the height of the cliff. 

Solution
Let D be the position of the man and AB be the water level and AB be the cliff. The angles of elevation of the top and depression of the base is 60° and 30.

straight i. straight e. space space space space space angle BDE space space space space equals space 60 degree space and space angle DEA space equals space 30 degree Let space space space space space space space space space BE space space space space space space equals space straight h space and space AC space space DE space equals straight x Now comma space space In space increment space BDE space tan space 60 degree space equals space BE over DE rightwards double arrow space space space space space space space space space space square root of 3 space space space space equals space space straight h over straight x rightwards double arrow space space space space space space space space space space space straight x space space space space equals space space fraction numerator straight h over denominator square root of 3 end fraction space space space space space space space space space space space space space space space space space space... left parenthesis straight i right parenthesis In space increment ADE comma space tan space 30 degree space equals space AE over DE rightwards double arrow space space space space space space space space space fraction numerator 1 over denominator square root of 3 end fraction equals 14 over straight x rightwards double arrow space space space space space space space space space space space straight x space space equals space 14 square root of 3 space space space space space space space space space space space space space space space space space space... left parenthesis ii right parenthesis
Comparing (i) and (ii), we get
fraction numerator straight h over denominator square root of 3 end fraction equals 14 square root of 3 rightwards double arrow space space space straight h space equals space 14 square root of 3 plus square root of 3 equals 42 space straight m
Hence, Height of the cliff.
= h + 14 = 42 + 14 = 56 m
And space distance space straight x space equals space fraction numerator straight h over denominator square root of 3 end fraction space space space space space space space space space space space space space space space space space space space space space equals space fraction numerator 42 over denominator square root of 3 end fraction equals fraction numerator 14 square root of 3 cross times square root of 3 over denominator square root of 3 end fraction space space space space space space space space space space space space space space space space space space space space space equals space 14 square root of 3 equals 14 space straight x space 1.732 space space space space space space space space space space space space space space space space space space space space space equals space 24.25 space straight m

Tips: -

open square brackets bold Take bold space square root of bold 3 bold equals bold 1 bold. bold 732 close square brackets

Some More Questions From Circles Chapter

In the following figure, what are the angles of depression from the observing positions O1 and O2 of the object at A?

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation