First slide

Applications of trigonometry

Question

A tree is leaning towards east. Two points due west of the tree are at distances ‘a’ and ‘b’ from its foot. If $α$ and $β$ are the elevations of the top of the tree from these points, its inclination to the horizon is

Difficult

A

$S i n^{- 1} (\frac{b - a}{b \cot α - a \cot β})$
B

$C o s^{- 1} (\frac{b - a}{b \cot α - a \cot β})$
C

$T a n^{- 1} (\frac{b - a}{b \cot α - a \cot β})$
D

$C o t^{- 1} (\frac{b - a}{b \cot α - a \cot β})$

Solution

$W e h a v e \tan α = \frac{h}{a + x} \Rightarrow a + x = h \cot α$ -----xb
$A l s o \tan β = \frac{h}{b + x} \Rightarrow b + x = h \cot β$ -------xa
$\Rightarrow x (b - a) = h (b \cot α - a \cot β)$
$\Rightarrow \frac{h}{x} = \frac{b - a}{b \cot α - a \cot β}$
$∴ \tan θ = \frac{b - a}{b \cot α - a \cot β} \Rightarrow θ = T a n^{- 1} (\frac{b - a}{b \cot α - a \cot β})$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App