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Answer:
no — the hypotenuse is about 33.5 ft long
Step-by-step explanation:
The hypotenuse (h) is given by the Pythagorean theorem.
h² = 15² +30² = 225 +900 = 1125
h = √1125 ≈ 33.54
The hypotenuse of this triangle is not 39 feet long.
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Additional comment
You can estimate the hypotenuse based on the relative side lengths. Here the short side is 1/2 the length of the long side. This means the hypotenuse will be longer than the long side by an amount between ...
0.4(1/2)² = 0.1
and
0.5(1/2)² = 0.125
times the length of the long side. That is, the additional length will be between 3 and 3.75 feet, so the hypotenuse will be shorter than 33.75 feet.
