Question

find the length of side $b$ in the right triangle, where the hypotenuse is 78cm and one right-angled side is 30cm.

Explanation:

Step1: Identify Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$

Step2: Rearrange to solve for $b$

$b = \sqrt{c^2 - a^2}$

Step3: Substitute given values

$b = \sqrt{78^2 - 30^2}$

Step4: Calculate squares

$78^2=6084$, $30^2=900$

Step5: Compute difference

$6084 - 900 = 5184$

Step6: Take square root

$\sqrt{5184}=72$

Answer:

$72\ \text{cm}$