A building is 2 ft from a 12 ft fence that surrounds the property. A worker wants to wash a window in the building 17 ft from th
e ground. He plans to place a ladder over the fence so it rests against the building. He decides he should place the ladder 8 ft from the fence for stability. To the nearest tenth of a foot, how long of a ladder will he need?
2 answers:
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<h3>Answer: 24 feet (Choice D)</h3>
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Explanation:
Refer to the diagram below. The goal is to find x, which is the horizontal distance from the base of the tree to the swing set.
Focus on triangle BCD.
The angle B is roughly 30.26 degrees, and this is the angle of depression. This is the amount of degrees Emir must look down (when starting at the horizontal) to spot the swing set.
We know that he's 14 ft off the ground, which explains why AB = CD = 14.
The goal is to find BC = AD = x.
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Again, keep your focus on triangle BCD.
We'll use the tangent ratio to say
tan(angle) = opposite/adjacent
tan(B) = CD/BC
tan(30.26) = 14/x
x*tan(30.26) = 14
x = 14/tan(30.26)
x = 23.9965714046732
That value is approximate. Make sure your calculator is in degree mode.
That value rounds to 24 feet when rounding to the nearest whole foot.
9514 1404 393
Answer:
58. 2 real roots; see attached for a graph
59. -6, 3
Step-by-step explanation:
58. A graphing calculator graphs this easily. The graph is shown in the attachment. There are 2 x-intercepts, hence 2 real roots.
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59. The x-intercepts are (-6, 0) and (3, 0), so the x-values x=-6 and x=3 satisfy the equation y = 0.
