f the distance to the bottom of the sun is approximately 90 million miles from Earth, and the angle of elevation to the top of the sun is 0.5 ∘, find the diameter of the sun. Round to the nearest 10, 000 miles.

Question

Mathematics

Manatee

1 March, 15:42

f the distance to the bottom of the sun is approximately 90 million miles from Earth, and the angle of elevation to the top of the sun is 0.5 ∘, find the diameter of the sun. Round to the nearest 10, 000 miles.

+2

Answers (1)

Know the Answer?

Audrina · Answer 1

790,000miles

Step-by-step explanation:

Given:

Angle of elevation = 0.5°

Distance = 90,000,000 miles

For the angle of elevation, we neet to convert it from degree to time.

Therefore to convert we use:

Angular size = 0.5° * (60min/degree) * (60seconds/min) =

= 0.5*60*60 = 1800 seconds of arc

Therefore, to find the diameter we use the formula:

Angular diameter = 206265 * (diameter of sun/distance)

Since we are looking for the diameter, we make it subject of the formula, we have:

Diameter of Sun = (Angular diameter * distance) / 206265

Applying the formula we have:

(1800*90000000) / 206265

= 785394.43

Which is approximately 790,000miles.

Therefore diameter of the sun is 790,000 miles