Question

hw 1.4

online homework for section 1.4.

• you have unlimited attempts, provided they are all done by the posted deadline.
• only the highest score of your attempts will count.
• each attempt will be limited to one hour.
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• each attempt will have similar, but different questions.
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1 formula 0.5 points

in a right triangle with side lengths of 30 cm and 77 cm, what is the length of the hypotenuse?

round your answer to the nearest hundredth, but do not include \cm\ with your response.

answer

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the Pythagorean theorem states that \( c = \sqrt{a^2 + b^2} \), where \( a \) and \( b \) are the legs and \( c \) is the hypotenuse. Here, \( a = 30 \) and \( b = 77 \).

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

\( a^2 = 30^2 = 900 \), \( b^2 = 77^2 = 5929 \). Then \( a^2 + b^2 = 900 + 5929 = 6829 \).

Step3: Find the square root

\( c = \sqrt{6829} \approx 82.64 \) (rounded to the nearest hundredth).

Answer:

82.64