Read the scenario and provide the missing numerical value to complete the sentence.

Cevap:A guy wire is securely attached to a vertical radio mast at a height of

60\text{ feet}

above the level ground. The other end of the wire is anchored to the ground exactly

25\text{ feet}

from the base of the mast. Assuming the mast is perfectly perpendicular to the ground, the length of the guy wire is 【65】 feet.

Cevap

The mast, the ground, and the guy wire form a right triangle where the mast and the ground act as the two legs, and the guy wire is the hypotenuse. Using the Pythagorean theorem (

a^2 + b^2 = c^2

), we substitute the given leg lengths:

25^2 + 60^2 = c^2

. This simplifies to

625 + 3600 = 4225

. The square root of

4225

65

, meaning the guy wire is

65\text{ feet}

long. Additionally, recognizing that the side lengths (

25, 60, 65

) are a multiple of the common

5-12-13

Pythagorean triple (each multiplied by

5

) provides a quick way to solve the problem without large calculations.

Adım Adım Çözüm

Identify the shape formed by the scenario.

A right triangle is formed by the vertical mast, the level ground, and the diagonal guy wire.

The mast is perpendicular to the ground, creating a 90-degree angle.

Set up the Pythagorean theorem equation.

a^2 + b^2 = c^2

, where

a = 25

and

b = 60

The legs of the right triangle are the distance along the ground (25 ft) and the height up the mast (60 ft). We need to find the hypotenuse,

c

Calculate the squares of the leg lengths.

25^2 = 625

and

60^2 = 3600

Squaring the values is required before adding them to find the square of the hypotenuse.

Add the squared values together.

625 + 3600 = 4225

This sum represents

c^2

, the square of the guy wire's length.

Find the square root of the sum to determine the final length.

\sqrt{4225} = 65

Taking the square root of

c^2

gives the actual length of the hypotenuse,

c

Anahtar Kavram

Pythagorean Theorem Application

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