Answer:
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
The diameter of the sun is equal to [tex]1.031*10^1^0 mi[/tex]
Data;
To solve this problem, we can use trigonometric ratio on this where the angle of elevation represents the angle, the diameter is represented by adjacent and the distance to the sun is represented by opposite.
Using SOHCAHTOA
since we have have angle and opposite, we can use tangent of the angle
[tex]tan \theta = \frac{opposite}{adjcent} \\tan 0.5 = \frac{90*10^6}{x} \\x = \frac{90*10^6}{tan 0.5} \\x = 1.031*10^1^0 miles[/tex]
The diameter of the sun is equal to [tex]1.031*10^1^0 mi[/tex]
Learn more on trigonometric ratio here;
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