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The elongation α
of a planet is the angle formed by the planet, earth, and sun. it is known that the distance from the sun to venus is 0.723au
(see exercise 65 in section 6.2 ). at a certain time the elongation of venus is found to be 39.4∘.
find the possible distances from the earth to venus at that time in astronomical units (au).

Answer :

MRROYALGO

The distance from the earth to venus is an illustration of the sine ratio

The distance from the earth to venus at that time is 1.12 au

How to determine the possibe distance?

See attachment for the diagram that illustrates the complete question.

Start by calculating the angle V using the following sine ratio

SE/sin(V) = VS/sin(E)

This gives

1/sin(V) = 0.723/sin(39.4)

Take the inverse of both sides

sin(V)/1 = sin(39.4)/0.723

Evaluate the quotient

sin(V) = 0.8779

Take the arcsin of both sides

V = 61.4

Calculate the measure of angle S

<S + <V + <E = 180

This gives

<S  = - <V - <E + 180

Substitute known values

<S  = -61.4 - 39.4 + 180

<S  = 79.2

The distance (VE) is then calculated using the following sine ratio

VE/sin(S) = VS/sin(E)

This gives

VE/sin(79.2) = 0.723/sin(39.4)

Multiply bot sides by sin(79.2)

VE = sin(79.2) * 0.723/sin(39.4)

Evaluate the product

VE = 1.12

Hence, the distance from the earth to venus at that time is 1.12 au

Read more about sine ratios at:

https://brainly.com/question/2920412

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