Question

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

(figure of right triangle with right angle at c, sides: a (bc), b (ac), c (ab))

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, the Pythagorean theorem states that \( c^{2}=a^{2}+b^{2} \), where \( a = 10.6 \), \( b = 24 \).
So we first calculate \( a^{2}=(10.6)^{2}=112.36 \) and \( b^{2}=(24)^{2} = 576 \).

Step2: Calculate \( c^{2} \)

Then \( c^{2}=a^{2}+b^{2}=112.36 + 576=688.36 \).

Step3: Find \( c \)

Take the square root of \( c^{2} \) to get \( c=\sqrt{688.36} \approx 26.24 \) (rounded to the nearest hundredth).

Answer:

\( 26.24 \)