Question

You are watching fireworks over San Diego Bay S as you sail away in a boat. The highest point the fireworks reach F is about 0.2 mile above the bay. Your eyes E are about 0.01 mile above the water, the lowest elevation from which you see the fireworks above your horizon. (At point B you cannot see the fireworks because of the curvature of Earth.) The radius of Earth is about 4000 miles, and FE¯¯¯¯¯¯¯¯ is tangent to Earth at point T. Find mSB⌢. Round your answer to the nearest tenth.

Answer 1

Answer:

no

Step-by-step explanation:

Answer 2

Based on the calculations, the measure of angle m<SB rounded to the nearest tenth is equal to 0.70°.

What is a tangent?

In geometry, a tangent is also referred to as a tangent line and it can be defined as a straight line that touches a plane curve at a specific point.

Based on the diagram, we would apply the cosine function to determine the measure of the angle formed by the hypotenuse side of the triangle with respect to the radius of Earth (adjacent side):

m<SB = cos⁻¹(4000/4000 + 0.2) + cos⁻¹(4000/4000 + 0.01)

m<SB = cos⁻¹(4000/4000.2) + cos⁻¹(4000/4000.01)

m<SB = cos⁻¹(0.99995) + cos⁻¹(0.9999975)

m<SB = 0.573 + 0.128

m<SB = 0.701 ≈ 0.70°.

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