Question

On a certain phase of the year, the sun(relative to Earth) forms a right angle with the moon as shown in the figure. If the distance from Earth to the moon is approximately $240,000$ miles, and the distance from the moon to the sun is approximately $91,674,000$ miles, Calculate the distance in miles between the Earth and the Sun during this phase.

• A. $84,042,000$
• B. $88,434,000$
• C. $91,674,000$
• D. $8,404,180,000$

Answer 1

Answer: (C)

$91,674,000$

The distance between the earth and the moon is given by $240,000$ miles.

The distance between the moon and the sun is given by $91,674,000$ miles.

During this phase, since the three form a right angled triangle,

distance between the Earth and the sun $=$ $\sqrt{(240000{)}^2+(91674000{)}^2}$

$=\sqrt{57600000000+8404122276000000}$

$=\sqrt{8404179876000000}$

$=91674314.14$ miles