The leg of a right-angled triangle is 10 cm, and its projection onto the hypotenuse is 8 cm.

univerkov | July 15, 2021 | education

The leg of a right-angled triangle is 10 cm, and its projection onto the hypotenuse is 8 cm. Find the length of the hypotenuse.

1. Vertices of the triangle – A, B, C. Angle A – straight line. AE – height. S – area. Length AB = 10

see BE = 8 cm.

2. Calculate the length of the height AE:

AB² – BE² = AE² (along the tower of Pythagoras).

AE = √AB² – BE² = √10² – 8² = √100 – 64 = √36 = 6 cm.

4. AE² = BE x CE (according to the properties of a right-angled triangle).

CE = 36: 8 = 4.5 cm.

5. We calculate the length of the segment of the hypotenuse BC:

BC = BE + CE = 8 + 4.5 = 12.5 cm.

Answer: the length of the hypotenuse BC = 12.5 cm.

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