Question

Which equation gives the length of the altitude of ABC?

Answer 1

B

Explanation:

`$(CD)/(AD) =(AD)/(BD) $`

`AD^2=CD \cdot BD`

`AD=√(CD \cdot BD)`

In this question, you are clearly supposed to use the geometric mean theorem or known as the right triangle altitude theorem. But note that there are other approaches to find the height of the triangle.

Using Pythagorean theorem:

`AD^2+CD^2=AC^2 \Rightarrow AD=√(AC^2-CD^2)`

Also,

`AD=AC\sin(c)`

Answer 2

B. AD = sqrt(CD * BD)

Explanation:

By the right triangle altitude theorem,

CD/AD = AD/BD

AD^2 = CD * BD

AD = sqrt(CD * BD)

Answer: B. AD = sqrt(CD * BD)