Question

emily is standing 150 feet from a circular target with radius 3 inches. will she hit the target if her aim is off by 0.2 degrees?

Answer 1

no

Explanation:

The angle subtended by the radius of the target at Emily's distance can be found using the tangent relation.

Application

tan(α) = opposite/adjacent = (1/4 ft)/(150 ft) = 1/600

The angle is found using the inverse relation:

α = arctan(1/600) ≈ 0.095°

If Emily's aim is off by 0.2°, she will miss the target by several inches.

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Additional comment

Emily's projectile will miss her aiming point by ...

(150 ft)tan(0.2°) ≈ 0.524 ft ≈ 6.28 in