Question

solve for x. round to the nearest tenth if necessary.
right triangle with legs 25 and x, hypotenuse 65
options:
x=35
x=45
x=60
x=65
x=70

Explanation:

Step1: Identify the triangle type

This is a right triangle, so we use the Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse, and \(a\), \(b\) are the legs. Here, \(a = 25\), \(c = 65\), and \(b = x\).

Step2: Rearrange the formula to solve for \(x\)

We get \(x^2 = c^2 - a^2\). Substitute the values: \(x^2 = 65^2 - 25^2\).

Step3: Calculate the squares

\(65^2 = 4225\) and \(25^2 = 625\). So \(x^2 = 4225 - 625 = 3600\).

Step4: Take the square root

\(x = \sqrt{3600} = 60\).

Answer:

\(x = 60\) (corresponding to the option "x = 60")