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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 [Take $\sin 110 ° = 0.939$ and $\sin 35 ° = 0.573$ ]

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12.2

miles

6.75

miles

7.00

miles

7.50

miles

answer is A.

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Detailed Solution

It is given that 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}

. AC

= 20

miles.

Draw a line through B parallel to AC.
Then,

C = 35 °

…. (alternate interior angle).
In

△ ABC,

Sum of all angles

= 180 °

⇒

∠ A + ∠ B + ∠ C = 180 °

⇒

35 ° + ∠ B + 35 ° = 180 °

⇒

∠ B = 180 ° - 70 °

⇒

∠ B = 110 °

We know, according to sin rule,

\frac{sinA}{BC} = \frac{sinB}{AC} = \frac{sinC}{AB}

⇒

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

⇒

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

⇒

AB = \frac{20 \times 0.573}{0.939}

[Take

\sin 110 ° = 0.939

and

\sin 35 ° = 0.573

]
⇒

AB = 12.2

miles
Hence, the correct option is 1.

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