Question

Calculate the shortest distance from surface of earth to moon, if the diameter(d) of earth is 12,700km and the angle $\left(\theta \right)$ between diameter and line of sight is ${88.97}^{\circ }$ as shown in the diagram.
$tan{89}^{\circ }=57.2$

• A. 3,84,970 km
• B. 7,54,870 km
• C. 2,14,475 km
• D. 1,54,370 km

Answer 1

The correct option is A

3,84,970 km

AD =Diameter of earth =13,700 km
AB=Radius of earth =6,850 km
BC =Distance from Moon to the center of Earth =6,850km + x
x =distance from moon to surface of Earth
Consider the $\Delta ABC$,
Its given that $\angle BAC=\theta ={89}^{\circ }$
$tan\theta =\frac{\text{opposite side}}{\text{adjacent side}}=\frac{BC}{AB}=\frac{6,850+x}{6,850}$
It's given in the question that $ta{n}^{\circ }=57.2$
Therefore,
$\frac{6,850+x}{6,850}=57.2$
6,850 +x = 57.2 $\times$ 6,850 km
6,850 + x = 3,91,820 km
x = 3,91,820 km - 6,850 km
x = 3,84,970 km