The height BD is drawn in a right-angled triangle ABC. Find the length of the hypotenuse AC

univerkov | May 20, 2021 | education

The height BD is drawn in a right-angled triangle ABC. Find the length of the hypotenuse AC if the angle ABD = 60, CD = 2cm

In a right-angled triangle BCD, the angle CBD = (90 – ABD) = (90 – 60) = 30.

Since the CD leg lies opposite the angle 30, the BC length = 2 * CD = 2 * 2 = 4 cm.

By the Pythagorean theorem, we determine the length of the leg BD. ВD ^ 2 = ВС ^ 2 – СD ^ 2 = 16 – 4 = 12.

ВD = 2 * √3 cm.

Right-angled triangles ABD and BCD are similar in acute angle.

Then BD / AD = CD / BD.

AD = BD ^ 2 / CD = 12/2 = 6 cm.

AC = AD + CD = 6 + 2 = 8 cm.

Answer: The length of the AC hypotenuse is 8 cm.

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