You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

General Solution of Trigonometric Equation

From the top ...

Question

From the top of the lighthouse, the angles of depression of two stations on the opposite sides of it at a distance $d$ apart are $α$ and $β .$ The height of the lighthouse is

\frac{d tan α}{tan α + tan β}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{d}{cot α + cot β}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{d tan β}{tan α + tan β}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{d cot α}{cot α + cot β}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $\frac{d}{cot α + cot β}$

$cot α = \frac{x}{h}, cot β = \frac{d - x}{h} h cot α = x, h cot β = d - x h = \frac{d}{cot α + cot β}$

Suggest Corrections

Similar questions

Q. From the top of a lighthouse, the angles of depression of two stations on opposite sides and

a

distance apart are

α

and

β

. The height of the lighthouse is:

Q. The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α. After walking a distance d towards the foot of the tower the angle of elevation is found to be β. The height of the tower is

(a)

\frac{d}{c o t α + c o t β}

(b)

\frac{d}{c o t α - c o t β}

(c)

\frac{d}{\tan β - \tan α}

(d)

\frac{d}{\tan β + \tan α}

From the top of a lighthouse, the angles of depression of two ships on the opposite sides of it are observed to be $α$ and $β$ . If the height of the lighthouse be h metres and the line joining the ships passes through the foot of the lighthouse, show that the distance between the ships is $\frac{h (t a n α + t a n β)}{t a n α t a n β}$ metres. [3 MARKS]

Q. A jet plane is at a vertical height of

h

. The angles of depression of two tanks on the horizontal ground are found to have measures

α

and

β, α > β

. Prove that the distance between the tanks is

\frac{h (tan α - tan β)}{tan α - tan β}

assuming both the tanks are on the same side of the jet plane.

Join BYJU'S Learning Program

From the top of the lighthouse, the angles of depression of two stations on the opposite sides of it at a distance d apart are α and β. The height of the lighthouse is

The correct option is B dcotα+cotβ cotα=xh,cotβ=d−xhhcotα=x,hcotβ=d−xh=dcotα+cotβ

From the top of the lighthouse, the angles of depression of two stations on the opposite sides of it at a distance $d$ apart are $α$ and $β .$ The height of the lighthouse is

The correct option is B $\frac{d}{cot α + cot β}$

$cot α = \frac{x}{h}, cot β = \frac{d - x}{h} h cot α = x, h cot β = d - x h = \frac{d}{cot α + cot β}$