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Answer :
Using the Pythagorean theorem, the length of the third side of the right triangle with a hypotenuse of 99.1 and one side of 7.0 units is found to be approximately 98.8 units after solving and rounding to the nearest tenth.
The student wants to find the length of the third side of a right triangle, knowing the length of the hypotenuse is 99.1 units and one side is 7.0 units. To solve this problem, we use the Pythagorean theorem, which states that the square of the hypotenuse (longest side) of a right triangle is equal to the sum of the squares of the other two sides.
The theorem is expressed as c^2 = a^2 + b^2 where c is the hypotenuse and a and b are the other two sides. Let's denote the unknown side as x. According to the Pythagorean theorem, we have:
- 99.1^2 = 7.0^2 + x^2
- x^2 = 99.1^2 - 7.0^2
- x^2 = 9819.21 - 49
- x^2 = 9770.21
- x = √9770.21
- x ≈ 98.8
Therefore, the length of the third side, rounded to the nearest tenth, is approximately 98.8 units.
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