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Answer:
x = -15 and x = 1
Step-by-step explanation:
Since we have to use the complete the square method, we first need to <u>rewrite the equation</u> in the form .
This results in .
Next, we <u>simplify the equation</u> to get .
<u>Factoring </u>the left side gives us .
Finally we <u>solve the equations</u>: and
.
This gives us x=1, and x=-15
<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.