CameraIcon

SearchIcon

MyQuestionIcon

229

You visited us 229 times! Enjoying our articles? Unlock Full Access!

Calculating Heights and Distances

The angle of ...

Question

The angle of elevation of the top of a tower from the bottom and top of a building of height $h m t$ are $α$ and $β$ respectively. The height of the tower is

A

\frac{h sin α cos β}{sin (α - β)}

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

B

∣ ∣ ∣ \frac{d sin α cos β}{cos (α + β)} ∣ ∣ ∣

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

C

∣ ∣ ∣ \frac{d cos α + sin β}{cos (α - β)} ∣ ∣ ∣

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

D

∣ ∣ ∣ \frac{d sin α - sin β}{sin (α - β)} ∣ ∣ ∣

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

Open in App

Solution

The correct option is A $\frac{h sin α cos β}{sin (α - β)}$
Given,
$∠ A B D = β, ∠ E C D = α, B C = h, A B = E C$

$⟹ A B = \frac{A D}{t a n β}$

$⟹ E C = \frac{E D}{t a n α} = \frac{A D - h}{t a n α}$

We know that $A B = E C$

$\frac{A D}{t a n β} = \frac{A D - h}{t a n α}$

Height of tower $A D = \frac{h t a n β}{t a n β - t a n α}$

$⟹ A D = \frac{h s i n α c o s β}{s i n (α - β)}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The elevation of a tower due North of a station

A

α

or (at a place due South of it is

α

) and at another station

B

A

β

. Prove that the height of the tower is

\frac{A B}{\sqrt{({cot}^{2} β - {cot}^{2} α)}}

\frac{A B tan α tan β}{\sqrt{({tan}^{2} α - {tan}^{2} β)}}

\frac{A B sin α sin β}{\sqrt{({sin}^{2} α - {sin}^{2} β)}}

\frac{A B sin α sin β}{{[sin (α + β) sin (α - β)]}^{1 / 2}}

{sin}^{2} α - {sin}^{2} β = sin (α + β) sin (α - β)

β

α

are +ive angles less than two right angles and

c o s α + c o s (α + β) + c o s (α + β + γ) = 0

s i n α + s i n (α + β) + s i n (α + β + γ) = 0

β = γ = 2 π / 3

α

β

are complementary angle such that qsin

α

= P , then find the value of

(sin α cos β - cos α sin β)

Q. Prove that if

α

β

γ

are angles of a triangle, then sin

α \times s i n β - c o s γ = c o s α c o s β

α

β

π < α - β < 3 π

sin α + sin β = - \frac{21}{65}

cos α + cos β = - \frac{27}{65}

, then the value of

cos \frac{(α - β)}{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Questions

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Calculating Heights and Distances

Standard X Mathematics

Join BYJU'S Learning Program

CrossIcon