Question

Solve for the missing side round to the nearest 10th (look at image)

Answer 1

• 14.3 yd

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Explanation :

• This is Right Angled Triangle.

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Solution :

• We'll solve this using the Pythagorean Theorem.

where,

• XY (3 yd) is the perpendicular

• YZ (14 yd) is the Base.

• XZ is the Hypotenuse.

We know that,

`{\longrightarrow \pmb{\mathbb {\qquad (XZ) {}^(2) = (XY) {}^(2) +( YZ) {}^(2) }}} \\ \\`

Now, we will substitute the given values in the formula :

`{\longrightarrow \sf{\pmb {\qquad (XZ) {}^(2) = (3) {}^(2) +( 14) {}^(2) }}} \\ \\`

We know that, (3)² = 9 and (14)² = 196. So,

`{\longrightarrow \sf{\pmb {\qquad (XZ) {}^(2) = 9 +196 }}} \\ \\`

Now, adding 9 and 196 we get :

`{\longrightarrow \sf{\pmb {\qquad (XZ) {}^(2) = 205 }}} \\ \\`

Now, we'll take the square root of both sides to remove the square from XZ :

`{\longrightarrow \sf{\pmb {\qquad \sqrt{(XZ) {}^(2)} = √(205 )}}} \\ \\`

When we take the square root of (XZ)² , it becomes XZ,

`{\longrightarrow \sf{\pmb {\qquad XZ = √(205 )}}} \\ \\`

We know that, square root of 205 is 14.317 (approx) .

`{\longrightarrow { \mathbb{\pmb {\qquad XZ }}}} \approx \pmb{\mathfrak{14.317 } }\\ \\`

So,

• The measure of the missing side (XZ) is 14.3 (Rounded to nearest tenth)

Answer 2

14.3

Explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

14^2 + 3^2 = c^2

196 + 9 = c^2

205 = c^2

Take the square root of each side

sqrt(205) = sqrt(c^2)

14.31782106 = c

Rounding to the nearest tenth

14.3 = c