Question

1. a right triangle is shown where the horizontal leg has a measure of 8.4 centimeters (cm), and the hypotenuse has a measure of 13.6 cm.

what is the length, in centimeters (cm), of the vertical leg?
____cm

Explanation:

Step1: Apply Pythagorean theorem

Let the vertical leg be \(a\), the horizontal leg \(b = 8.4\) cm, and the hypotenuse \(c=13.6\) cm. According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), so \(a^{2}=c^{2}-b^{2}\).

Step2: Substitute values

Substitute \(b = 8.4\) and \(c = 13.6\) into the formula: \(a^{2}=(13.6)^{2}-(8.4)^{2}\).

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Step3: Calculate \(a\)

Take the square root of \(a^{2}\): \(a=\sqrt{114.4}\approx10.7\) (rounded to one decimal place).

Answer:

\(10.7\)