Question

Can someone please give me the (Answers) to this? ... please ...

I need help….

Answer 1

Answers:

1. Height =
   `3√(15)` feet
2. Distance they run = 150 meters
3. Exactly 9 feet away from the base.
4. Exact length is
   `5√(13)` feet

The diagrams for each are shown below (attached image).

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Work Shown:

Problem 1

• a = 3
• b = unknown
• c = 12

`a^2 + b^2 = c^2\\\\3^2 + b^2 = 12^2\\\\9 + b^2 = 144\\\\b^2 = 144 - 9\\\\b^2 = 135\\\\b = √(135)\\\\b = √(9*15)\\\\b = √(9)*√(15)\\\\b = 3√(15)\\\\`

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Problem 2

• a = 90
• b = 120
• c = unknown

`a^2 + b^2 = c^2\\\\90^2 + 120^2 = c^2\\\\8100 + 14400 = c^2\\\\22500 = c^2\\\\c^2 = 22500\\\\c = √(22500)\\\\c = 150\\\\`

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Problem 3

• a = unknown
• b = 12
• c = 15

`a^2 + b^2 = c^2\\\\a^2 + 12^2 = 15^2\\\\a^2 + 144 = 225\\\\a^2 = 225 - 144\\\\a^2 = 81\\\\a = √(81)\\\\a = 9\\\\`

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Problem 4

• a = 10
• b = 15
• c = unknown

`a^2 + b^2 = c^2\\\\10^2 + 15^2 = c^2\\\\100 + 225 = c^2\\\\325 = c^2\\\\c^2 = 325\\\\c = √(325)\\\\c = √(25*13)\\\\c = √(25)*√(13)\\\\c = 5√(13)\\\\`

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Side notes:

• When simplifying the square root, the idea is to pull out the largest perfect square factor if possible. Then I used the rule that
  `√(x*y) = √(x)*√(y)` to break up the roots.
• I have 'a' as the horizontal leg and b as the vertical leg in each of the drawings below. The order doesn't matter but I did this to stay consistent.
• When applying the pythagorean theorem
  `a^2+b^2 = c^2`, the value of c is always the longest side (aka hypotenuse). This side is always opposite the 90 degree angle.