A tower subtends angles alpha, 2 alpha and 3 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) In $	riangle ECD$,$	an 3 \alpha = \frac{h}{CD} \Rightarrow CD = h \cot 3 \alpha \quad \dots(i)$In $	riangle EBD$,$	an 2 \alpha = \frac{h}{BD}

Vedclass · Accepted Answer

$1+2 \cos 2 \alpha$

Vedclass · Answer

(B) In $	riangle ECD$,$	an 3 \alpha = \frac{h}{CD} \Rightarrow CD = h \cot 3 \alpha \quad \dots(i)$In $	riangle EBD$,$	an 2 \alpha = \frac{h}{BD} \Rightarrow BD = h \cot 2 \alpha \quad \dots(ii)$In $	riangle EAD$,$	an \alpha = \frac{h}{AD} \Rightarrow AD = h \cot \alpha \quad \dots(iii)$From Eqs. $(ii)$ and $(iii)$,$AB = AD - BD = h(\cot \alpha - \cot 2 \alpha) \quad \dots(iv)$From Eqs. $(i)$ and $(ii)$,$BC = BD - CD = h(\cot 2 \alpha - \cot 3 \alpha) \quad \dots(v)$Dividing $(iv)$ by $(v)$:$\frac{AB}{BC} = \frac{\cot \alpha - \cot 2 \alpha}{\cot 2 \alpha - \cot 3 \alpha} = \frac{\frac{\cos \alpha}{\sin \alpha} - \frac{\cos 2 \alpha}{\sin 2 \alpha}}{\frac{\cos 2 \alpha}{\sin 2 \alpha} - \frac{\cos 3 \alpha}{\sin 3 \alpha}}$$= \frac{\frac{\sin(2 \alpha - \alpha)}{\sin \alpha \sin 2 \alpha}}{\frac{\sin(3 \alpha - 2 \alpha)}{\sin 2 \alpha \sin 3 \alpha}} = \frac{\sin \alpha}{\sin \alpha \sin 2 \alpha} 	imes \frac{\sin 2 \alpha \sin 3 \alpha}{\sin \alpha} = \frac{\sin 3 \alpha}{\sin \alpha}$$= \frac{3 \sin \alpha - 4 \sin^3 \alpha}{\sin \alpha} = 3 - 4 \sin^2 \alpha = 3 - 2(1 - \cos 2 \alpha) = 1 + 2 \cos 2 \alpha$.

$A$ tower subtends angles $\alpha, 2 \alpha$ and $3 \alpha$ respectively at points $A, B$ and $C$,all lying on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to:

Similar Questions

The angle of elevation of the top of a tower from a point $A$ due north of it is $\alpha$ and from a point $B$ at a distance of $9$ units due west of $A$ is $\cos^{-1}\left(\frac{3}{\sqrt{13}}\right)$. If the distance of the point $B$ from the tower is $15$ units,then $\cot \alpha$ is equal to.

The angles of elevation of the top of a tower $A$ from the top $B$ and bottom $D$ of a building of height $a$ are $30^\circ$ and $45^\circ$ respectively. If the tower and the building stand at the same level,then the height of the tower is

If the angles of depression of the top and bottom of a short building from the top of a tall building are $30^{\circ}$ and $60^{\circ}$ respectively,then the ratio of the heights of the short and tall buildings is

$A$ tower subtends angles $\alpha, 2\alpha, 3\alpha$ respectively at points $A, B$ and $C$,all lying on a horizontal line through the foot of the tower. Then $AB/BC = $

$A$ person standing on the bank of a river observes that the angle subtended by a tree on the opposite bank is $60^\circ$. When he moves $40 \ m$ away from the bank,he finds the angle to be $30^\circ$. The breadth of the river is.....$m$

Vedclass Test Series

Exam Paper Generator

Online Exam Module