Question

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Answer 1

12.4 yd

Explanation:

We use the Pythagorean Theorem

a² + b² = c²

Let's solve

3² + 12² = c²

9 + 144 = c²

153 = c²

c = 12.4 yd

Answer 2

The missing side length of the given right triangle is 12.4 yd to the nearest tenth.

Explanation:

Pythagoras Theorem

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The square of the hypotenuse (longest side) is equal to the sum of the squares of the legs of a right triangle.

`\boxed{a^2+b^2=c^2}`

where:

• a and b are the legs of the right triangle.
• c is the hypotenuse (longest side) of the right triangle.

As we have been given the lengths of both legs of the right triangle, we can use Pythagoras Theorem to calculate the length of the hypotenuse.

Substitute a = 3 and b = 12 into the formula and solve for c:

`\implies 3^2+12^2=c^2`

`\implies 9+144=c^2`

`\implies 153=c^2`

`\implies c=√(153)`

`\implies c=12.3693168...`

`\implies c=12.4\; \sf yd\;(nearest\;tenth)`

Therefore, the missing side length of the given right triangle is 12.4 yd to the nearest tenth.