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555-605 (Medium)|   Geometry|      
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Bunuel
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The image of a star is projected onto a planetarium wall by a projecto 08 Jun 2022, 12:45
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35% (medium)

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71% (01:54) correct 29% (02:38) wrong based on 28 sessions

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The image of a star is projected onto a planetarium wall by a projector that sits atop a vertical 4-foot stand. If the projector is directed 30 degrees above the horizontal, and the image appears 16 feet above the level floor of the planetarium, then, in feet, how far is the projector from the wall?


A. \(12\sqrt{2}\)

B. \(12\sqrt{3}\)

C. \(16\sqrt{2}\)

D. \(16\sqrt{3}\)

E. 24
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The image of a star is projected onto a planetarium wall by a projecto 08 Jun 2022, 13:05
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Bunuel
The image of a star is projected onto a planetarium wall by a projector that sits atop a vertical 4-foot stand. If the projector is directed 30 degrees above the horizontal, and the image appears 16 feet above the level floor of the planetarium, then, in feet, how far is the projector from the wall?


A. \(12\sqrt{2}\)

B. \(12\sqrt{3}\)

C. \(16\sqrt{2}\)

D. \(16\sqrt{3}\)

E. 24
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If the top of the projector is at 4 feet and the image is at 16 feet, the height of the triangle is 12. We are told that the angle is 30 degrees above horizontal, so we have a 30-60-90 triangle. We can therefore fill in the other sides. The hypotenuse is 24 and the base is \(12\sqrt{3}\). We are asked for the base.

Answer choice B.
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The image of a star is projected onto a planetarium wall by a projecto 12 Aug 2025, 03:43
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