Question

solve the right triangle shown in the figure.
a = 10.6, b = 24

a. what is the length of the side?
c ≈ \boxed{} (round to the nearest hundredth as needed.)

Explanation:

Step1: Apply Pythagorean theorem

In a right triangle, \( c^2 = a^2 + b^2 \). Given \( a = 10.6 \) and \( b = 24 \), substitute these values:
\( c^2 = (10.6)^2 + (24)^2 \)
Calculate \( (10.6)^2 = 112.36 \) and \( (24)^2 = 576 \). Then, \( c^2 = 112.36 + 576 = 688.36 \).

Step2: Solve for \( c \)

Take the square root of \( 688.36 \):
\( c = \sqrt{688.36} \approx 26.24 \)

Answer:

\( c \approx \boxed{26.24} \)