The leg of a right-angled triangle is 8, and its projection onto the hypotenuse is 4 cm. Find the hypotenuse.

univerkov | March 1, 2021 | education

1. A, B, C – the vertices of the triangle. Angle С = 90. Leg ВС = 8 cm. СН – height drawn to AB. BH = 4 cm.

2. We calculate the length of the CH height using the formula of the Pythagorean theorem:

CH = √BC² – BH² = √8² – 4² = √64 – 16 = √48 = 4√3 cm.

3. The length of the CH height is calculated by the formula:

CH = √AB x BH.

4. AH = CH²: BH = (4√3) ²: 4 = 12 cm.

5.AB = BH + AH = 4 + 12 = 16 cm.

Answer: the hypotenuse AB is 16 cm.

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