Question

Points A and C lie on a straight road and point B lies directly above the road. The angle of elevation from point A to point B is ${35}^{\circ }$ and the angle of depression from point B to point C is ${35}^{\circ }$. If the distance from A to C is $20$ miles. The distance between A and B is

• A. $12.25$
• B. $6.75$
• C. $7.00$
• D. $7.50$

Answer 1

The correct option is A $12.25$

In $△ABC,$

Sum of all angles $=180°$

$\Rightarrow \angle A+\angle B+\angle C=180°$

$\Rightarrow 35°+\angle B+35°=180°$

$\Rightarrow \angle B=180°-70°$

$\Rightarrow \angle B=110°$

Now, according to sin rule,

$\Rightarrow \frac{\sin A}{BC}=\frac{\sin B}{AC}=\frac{\sin C}{AB}$

$\Rightarrow \frac{\sin 110°}{20}=\frac{\sin 35°}{AB}$

$\Rightarrow AB=\frac{20\times \sin 35°}{\sin 110°}$

$\Rightarrow AB=12.25miles$

Hence, the answer is $\mathrm{12.25.}$