Question

1. choose the correct answer.

if one leg of a right triangle has a measure of 7 cm and the other leg has a measure of 9 cm,
what is the measure of the hypotenuse, rounded to one decimal place?
4 cm
16 cm
11.4 cm
5.7 cm

1. choose the correct answer.

if the hypotenuse of a right triangle has a measure of 8 feet and one leg has a measure of 4
feet, what is the measure of the other leg, rounded to one decimal place?
6.9 feet
12 feet
8.9 feet
6 feet

Explanation:

Step1: Apply Pythagorean theorem for first problem

For a right - triangle with legs \(a = 7\) and \(b = 9\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\). Substitute \(a = 7\) and \(b = 9\) into the formula: \(c=\sqrt{7^{2}+9^{2}}=\sqrt{49 + 81}=\sqrt{130}\).

Step2: Calculate the value of \(\sqrt{130}\)

\(\sqrt{130}\approx11.4\) (rounded to one decimal place).

Step3: Apply Pythagorean theorem for second problem

For a right - triangle with hypotenuse \(c = 8\) and one leg \(a = 4\), using the formula \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(c = 8\) and \(a = 4\) into the formula: \(b=\sqrt{8^{2}-4^{2}}=\sqrt{64 - 16}=\sqrt{48}\).

Step4: Calculate the value of \(\sqrt{48}\)

\(\sqrt{48}\approx6.9\) (rounded to one decimal place).

Answer:

1. \(11.4\) cm; 4) \(6.9\) feet