Q. 184.0( 2 Votes )

# 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. √2 ametres

B.

C.

D. 2 ametres

Answer :

Let AB and CD be the two poles of height h meters and 2h meters respectively such that BD be a km i.e.; the distance between the two poles and P be the midpoint of BD .

Given ∠APB = θ and ∠CPD = 90 – θ

In Δ ABP

tan θ =

tan θ = …………………1

In Δ CDP

cot (90° – θ) = PD / CD =

cot (90° – θ )=

tan θ = ………….2

Equating 1 and 2

=

8 h ^{2} = a^{2}

h = m

Rate this question :

Express the following as trigonometric ratio of complementary angle of 90^{o}- θ.

(i) tan (90^{o}- θ)

(ii) cos (90^{o}- θ)

If A+B=90^{o}, then fill up the blanks with suitable trigonometric ratio of complementary angle of A or B.

(i) sin A =…. (ii) cos B =…

(iii) sec A =… (iv) tan B =…

(v) cosec B =… (vi) cot A=…

KC Sinha - MathematicsFind the value of

(i) (ii)

(iii) (iv)

(v) (vi)

(vii) (viii)

(ix) sin 54° – cos 36° (x)

(xi) cosec 31° – sec 59° (xii)

(xiii)

KC Sinha - MathematicsIf cos 47^{o}=a, then express sin 43^{o} in terms of a.

If sin 56^{o}=x, then express sin 34^{o} in terms of x.

Fill up the blanks :

(i) If sin 50^{o}=0.7660, then cos 40^{o}=……

(ii) If cos 44^{o} = 0.7193, then sin 46^{o}=…..

(iii) sin 50^{o}+cos 40^{o} = 2 sin (………)

(iv) Value of is ………

KC Sinha - MathematicsProve that :

sin 9°. sin 27°. sin 63°. sin 81°

= cos9°.cos27°.cos63°.cos81°

KC Sinha - Mathematics