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Zorluk: KolayTriangles and Pythagorean Theorem

A theater crew is building a wooden stage prop in the shape of a right triangle. The vertical height of the prop is 1212 feet and the horizontal base is 55 feet. What is the length of the slanted top edge of the prop?

  1. A
    169169 feet
  2. B
    1717 feet
  3. 1313 feetCevap
  4. D
    119119 feet

Cevap

The length of the slanted top edge is 1313 feet.
The slanted edge represents the hypotenuse of a right triangle. According to the Pythagorean theorem, the square of the hypotenuse equals the sum of the squares of the two perpendicular legs (a2+b2=c2a^2 + b^2 = c^2). Substituting the given legs (55 and 1212), we calculate 52+122=25+144=1695^2 + 12^2 = 25 + 144 = 169. Taking the square root of 169169 yields 1313 feet.

Adım Adım Çözüm

1
Identify the given values as the legs of a right triangle.
The legs are a=5a = 5 and b=12b = 12. The unknown slanted edge is the hypotenuse, cc.
The Pythagorean theorem relates the two perpendicular legs to the longest side.
2
Substitute the leg values into the Pythagorean theorem formula, a2+b2=c2a^2 + b^2 = c^2.
52+122=c25^2 + 12^2 = c^2
This sets up the equation to solve for the missing hypotenuse.
3
Square the numbers and add them together.
25+144=c225 + 144 = c^2, which simplifies to 169=c2169 = c^2.
This isolates c2c^2 on one side of the equation.
4
Take the square root of both sides to find the value of cc.
c=13c = 13
Taking the square root cancels the exponent and gives the final length of the edge.

Anahtar Kavram

Using the Pythagorean theorem to calculate the hypotenuse of a right triangle.
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Konular

Triangles and Pythagorean Theorem

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