Given ΔABC, angle B = 90 °; AD = 4 cm, CD = 16 cm, BD – height. Find BD.

univerkov | April 4, 2021 | education

Since BD is height, triangles ABD and BCD are rectangular.

Let the angle BAD = X0, then the angle ABD = (90 – X).

In the triangle BCD, the angle CBD = (90 – ABD) = (90 – (90 – X)) = X0.

Then right-angled triangles ABD and CBD are similar in acute angle.

From the similarity of triangles: CD / BD = BD / AD.

BD ^ 2 = AD * CD = 4 * 16 = 64.

ВD = 8 cm.

Answer: The length of the height BD is 8 cm.

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