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Morgarella [4.7K]
4 years ago
8

Find the answers and explanation please

Mathematics
1 answer:
jeka57 [31]4 years ago
5 0
Length of ST = 13 (4 units above horizon + 9 units below = full length)

Length of OP = 13

Length of SP = 8 (1 unit left from vertical origin + 7 units right)

Length of TO = 8

Perimeter = 42 units (sum of all)

Area = 104 units sq.
(length * width = 13 * 8)
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x=6

Step-by-step explanation:

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Using cross products

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3 years ago
Determine the value of x.
Akimi4 [234]

Answer:   \frac{10}{\sqrt{3}}

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======================================================

Explanation:

To get the first value mentioned above, we simply divide the long leg (10) over the square root of 3.

This is due to the fact that if x is the short leg, then x*sqrt(3) is the long leg. We go in reverse of this process to go from long leg to short leg.

The expression \frac{10}{\sqrt{3}} is the same as \frac{10\sqrt{3}}{3} after we multiply top and bottom by sqrt(3) to rationalize the denominator.

Side notes:

  • This entire process only applies to 30-60-90 triangles.
  • The hypotenuse of a 30-60-90 triangle is twice as long as the short leg, so the hypotenuse is 2x = 2*\frac{10\sqrt{3}}{3} = \frac{20\sqrt{3}}{3}  units long.
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