February 22, 2017

Homework Help: Third Side, Reply to Jen

Posted by Count Iblis on Saturday, November 11, 2006 at 10:07am.

Hi Jen,

I've seen the drawing. My site is down at the moment.

Draw a line from Venus (either of the two positions) to the line Earth-Sun at right angles.

Let's call the distance Earth Venus d. Then you have a right angle triangle with a hypotenuse d, the line that intersects the line Sun Earth at right angles has a length of
d sin(30°)= d/2 and the distance from the Earth to the point where that line of length d/2 intersects the line Earth Sun (let's call it P) is
d cos(30°) =1/2 sqrt(3)d

The distance from the sun to P is then 1.5*10^8 km minus 1/2 sqrt(3)d

Now the line Sun-Venus is the hypotenuse of another right angled triangle with sides Sun to P and the line of length d/2 you've drawn.

This means that

(1.5*10^8 km - 1/2 sqrt(3)d)^2 + (d/2)^2 = (distance from sun to venus) squared

You can then solve d from this quadratic equation.

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