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KengaRu [80]
2 years ago
7

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

Mathematics
2 answers:
lions [1.4K]2 years ago
6 0

Answer :

  • 14.3 yd

⠀

Explanation :

  • This is Right Angled Triangle.

⠀

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}} =  \sqrt{205 }}}} \\ \\

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

{\longrightarrow  \sf{\pmb {\qquad XZ =  \sqrt{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 <em>(Rounded to nearest tenth)</em>
SIZIF [17.4K]2 years ago
3 0

Answer:

14.3

Step-by-step 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

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