The bottom of a large theater screen is 3ft above your eye level and the top of the acreen is 10ft above your eye level. Assume you walk away from the screen (perpendicular to the screen) at a rate of 3ft/s while looking at the screen. What is the change of the viewing angle when you are 30ft from the wall on which the screen hangs assuming the floor is horizontal?

Question

Sara Dixon

Mathematics

25 May, 00:06

The bottom of a large theater screen is 3ft above your eye level and the top of the acreen is 10ft above your eye level. Assume you walk away from the screen (perpendicular to the screen) at a rate of 3ft/s while looking at the screen. What is the change of the viewing angle when you are 30ft from the wall on which the screen hangs assuming the floor is horizontal?

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Kenyon Castro · Answer 1

tan (α) = 3x ⟹ dα dx = - 3 9 + x2 tan⁡ (α) = 3x ⟹ dα dx = - 3 9 + x2 tan (α+θ) = 13x ⟹ dθ dx + dα dx = - 13 169 + x2 tan⁡ (α+θ) = 13x ⟹ dθ dx + dα dx = - 13 169 + x2 dθ dx = - 13 169 + x2 + 3 9 + but the actual answer is you have to use this formula (with respect to tt), not an xx derivative. So you'll have to take into account that dx dt = 3 dx dt = 3 ft/sec