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CBSE Class 10 Answered

Ch-10 Height And Distance Doubt
question image
Asked by ctmonasara914 | 15 Feb, 2019, 09:58: PM
answered-by-expert Expert Answer
As shown in figure, Let AD is leaning tower inclined at an angle θ with horizontal. B and C are stations
which are at distances b and a respectively from foot of tower.

Let α and β are the angle of elevation of top of tower observed from C and B respectively.
 
Let OD = h and OA = x;
 
we have,
begin mathsize 12px style tan space theta space equals space h over x space semicolon space space c o t space theta space equals space x over h space
tan space alpha space equals space fraction numerator h over denominator x plus a end fraction space space space semicolon space space space space c o t space alpha space equals space x over h plus a over h space space space semicolon space space
c o t space alpha space equals space c o t space theta space plus space a over h space space..................... left parenthesis 1 right parenthesis

tan space beta space equals space fraction numerator h over denominator x plus b end fraction space space semicolon space space space c o t space beta space equals space x over h plus b over h semicolon space space space
c o t space beta space equals space c o t space theta space plus space b over h space space......................... left parenthesis 2 right parenthesis

M u l t i p l y space e q n. left parenthesis 1 right parenthesis space b y space b comma space space space b space c o t space alpha space equals space b space c o t space theta space plus space fraction numerator b a over denominator h end fraction space.............. left parenthesis 3 right parenthesis
M u l t i p l y space e q n. left parenthesis 2 right parenthesis space b y space a comma space space a space c o t space beta space equals space a space c o t space theta space plus space fraction numerator a b over denominator h end fraction space space............... left parenthesis 4 right parenthesis

s u b t r a c t space left parenthesis 4 right parenthesis space f r o m space left parenthesis 3 right parenthesis comma space space b space c o t space alpha space minus space a space c o t space beta space equals space left parenthesis b minus a right parenthesis space c o t space theta

h e n c e space c o t space theta space equals space fraction numerator b space c o t space alpha space minus space a space c o t space beta over denominator left parenthesis space b minus a space right parenthesis end fraction end style
Answered by Thiyagarajan K | 17 Feb, 2019, 10:27: AM
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