Question

in a right - triangle with sides $a = 3$, $b = 4$, what is the length of the hypotenuse $c$?
a. 5
b. 7
c. 8
d. 6
what happens if $a^{2}+b^{2}a. the triangle is isosceles
b. the triangle is acute
c. the triangle is equilateral
d. the triangle is obtuse

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), the Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\). Given \(a = 3\) and \(b = 4\), we substitute these values: \(3^{2}+4^{2}=9 + 16=25\), so \(c=\sqrt{25}=5\).

Step2: Recall triangle - type rules

If \(a^{2}+b^{2}

Answer:

a. 5
d. The triangle is obtuse