Question

solve problems involving right triangles. determine the length of the unknown side of the following triangles. a. triangle with legs 12 cm and 9 cm b. right triangle with hypotenuse 61 mm and one leg 6 cm c. is the triangle with side length 5 m, 10 m, and 15 m a right triangle? hand-drawn triangle with sides 5m, 10m, 15m

Explanation:

Part a

Step1: Identify the triangle type

This is a right triangle, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(a = 9\) cm, \(b = 12\) cm, and \(c\) is the hypotenuse (unknown side).

Step2: Apply the Pythagorean theorem

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Step1: Identify the triangle type and sides

This is a right triangle. Let the hypotenuse \(c = 61\) mm, one leg \(a = 60\) mm (wait, the given leg is 6 cm, convert to mm: \(6\) cm \(= 60\) mm), and the other leg \(b\) is unknown. Use the Pythagorean theorem: \(a^2 + b^2 = c^2\), so \(b^2=c^2 - a^2\).

Step2: Apply the formula

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Step1: Recall the Pythagorean theorem for right triangles

For a triangle with sides \(a\), \(b\), \(c\) (where \(c\) is the longest side), it is a right triangle if \(a^2 + b^2 = c^2\). Here, \(a = 5\) m, \(b = 10\) m, \(c = 15\) m.

Step2: Check the Pythagorean theorem

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And \(15^2 = 225\). Since \(125
eq225\) (i.e., \(5^2 + 10^2
eq15^2\)), the triangle does not satisfy the Pythagorean theorem.

Answer:

The length of the unknown side (hypotenuse) is 15 cm.

Part b