Finding a distance based on angle provided.

Question

The diameter of a spherical balloon is 44 m. How far away the balloon is on the sky when the opening angle where it was seen was 14∘? 
Give the answer using two significant figures. Please show work.

Answer

Step 1: Divide the diameter of the balloon by 2 to get the radius of the balloon. In this case, the radius is 44/2 = 22 meters.
Step 2: Divide the opening angle by 2 to get the half-angle. In this case, the half-angle is 14/2 = 7 degrees.
Step 3: Convert the angle in degrees to radians. 7 degrees is approximately 0.1219 radians
Step 4: use the tan function to get the tangent of the half-angle. In this case, tan(0.1219) = 0.1219
Step 5: Divide the radius of the balloon by the tangent of the half-angle. In this case, 22 / 0.1219 = 180.6 m

Answer

Chord = 2 r sin (c/2)Here, the diameter of the balloon is the chord through the opening angle. So, radius r = 44 m / ( 2 x sin (14∘/2)) = 22/sin 7∘ m = 180.52 mThus,  the balloon is 180.52m far away on the sky

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Finding a distance based on angle provided.

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