Question

what is the length of the missing leg in a right triangle if the hypotenuse is 13 units and one leg is 12 units?
a. 5 units
b. 7 units
c. 8 units
d. 10 units

in a right triangle, the hypotenuse is 10, and one leg is 6. what is the other leg?
a. 5
b. 3
c. 7
d. 8

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with hypotenuse \(c\) and legs \(a\) and \(b\), \(a^{2}+b^{2}=c^{2}\). Let the unknown leg be \(x\).

Step2: First problem

Given \(c = 13\) and one leg \(a = 12\). Then \(x^{2}=c^{2}-a^{2}\). Substitute the values: \(x^{2}=13^{2}-12^{2}=169 - 144=25\). So \(x=\sqrt{25}=5\).

Step3: Second problem

Given \(c = 10\) and one leg \(a = 6\). Then \(x^{2}=c^{2}-a^{2}\). Substitute the values: \(x^{2}=10^{2}-6^{2}=100 - 36 = 64\). So \(x=\sqrt{64}=8\).

Answer:

1. a. 5 units
2. d. 8 units