Question

solve for c.
triangle with legs 10 and 7, right angle, hypotenuse c
c = ?
pythagorean theorem: ( a^2 + b^2 = c^2 )
round your answer to the nearest hundredth.

Explanation:

Step1: Identify a, b, c

In a right triangle, \(a = 10\), \(b = 7\), \(c\) is hypotenuse. Use Pythagorean theorem \(a^2 + b^2 = c^2\).
\(10^2 + 7^2 = c^2\)

Step2: Calculate \(a^2 + b^2\)

\(10^2 = 100\), \(7^2 = 49\), so \(100 + 49 = c^2\)
\(149 = c^2\)

Step3: Solve for c

Take square root: \(c = \sqrt{149}\)
\(c \approx 12.21\) (rounded to nearest hundredth)

Answer:

\(12.21\)