In the rectangular ABC the length of the leg AB is 18, and its projection Ad onto the hypotenuse is 10.8.

| December 29, 2020 | education

In the rectangular ABC the length of the leg AB is 18, and its projection Ad onto the hypotenuse is 10.8. Find the length of the hypotenuse AC.

1. Applying the Pythagorean theorem, we calculate the length of the ВD leg of a right-angled AВD triangle:
BD = √AB ^ 2 – AD ^ 2 = √18 ^ 2 – 10.8 ^ 2 = √324 – 116.64 = √207.36 = 14.4 centimeters.
2. Using the formula for calculating the height, drawn from the vertex of the right angle to the hypotenuse,
we calculate the length of the segment of the CD:
BD = √AD x CD; BD ^ 2 = AD x CD
CD = BD ^ 2 / AD = 14.4 ^ 2 / 10.8 = 207.36 / 10.8 = 19.2 centimeters.
3. Calculate the length of the AC hypotenuse:
AC = BP + CD = 10.8 + 19.2 = 30 centimeters.
Answer: the length of the AC hypotenuse is 30 centimeters.



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