Question

A scientist measures the angle x and the distance y between the Earth and the Sun. Using complete sentences, explain how the scientist can use only these two measurements to calculate the distance between the Sun and the shooting star.

Answer 1

We know that :

$\spadesuit$  $Cos\theta = \frac{Adjacent Side}{Hypotenuse}$

Here Adjacent Side is BC, which is Distance between the Sun and Earth

Hypotenuse is CA, which is Distance between the Sun and Shooting star

⇒ $Cosx = \frac{BC}{CA}$

Given : Distance between Earth and Sun (BC) = y

⇒ $Cosx = \frac{y}{Distance\;between\;the\;Sun\;and\;Shooting\;Star}$

⇒ $Distance\;between\;the\;Sun\;and\;Shooting\;Star = \frac{y}{Cosx}$