Question 10 (Choice 1) - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [Term 2] - Solutions of Sample Papers for Class 10 Boards

Last updated at May 29, 2023 by Teachoo

Two vertical poles of different heights are standing 20m away from each other on the level ground. The angle of elevation of the top of the first pole from the foot of the second pole is 60° and angle of elevation of the top of the second pole from the foot of the first pole is 30°. Find the difference between the heights of two poles. (Take √3 = 1.73)

Question 10 (Choice 1) Two vertical poles of different heights are standing 20m away from each other on the level ground. The angle of elevation of the top of the first pole from the foot of the second pole is 60° and angle of elevation of the top of the second pole from the foot of the first pole is 30°. Find the difference between the heights of two poles. (Take √3 = 1.73)
Let two poles be AB & CD
Given, Length of the road = 20m
So, BC = 20 m
Also, ∠ACB = 30° & ∠DBC = 60°
We need to find difference between heights of the poles
i.e. CD − AB
In right angle triangle ABC,
tan C = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐶)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐶)
tan 30° = 𝑨𝑩/𝑩𝑪
(" " 1)/√3 = 𝐴𝐵/20
20/√3 = AB
AB = 𝟐𝟎/√𝟑
Now, in right angle triangle DBC
tan D = (𝑆𝑖𝑑𝑒 𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐷)/(𝑆𝑖𝑑𝑒 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑎𝑛𝑔𝑙𝑒" " 𝐷)
tan 60° = 𝑪𝑫/𝑩𝑪
√3 = 𝐶/20
20 √3 = CD
CD = 20√𝟑
Now,
Difference between heights = CD − AB
= 20√3 − 20/√3
= 20(√𝟑 −𝟏/√𝟑)
= 20( (√3 (√3) − 1)/√3)
= 20( (3 − 1)/√3)
= 20( 2/√3)
= 20( 2/√3 ×√3/√3)
= (𝟒𝟎√𝟑)/𝟑 cm
= (40 × 1.73)/3 cm
= 69.2/3 cm
= 23.06 cm

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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