Question

question 10 of 25
in the diagram below, $overline{bc}$ is an altitude of $\triangle abd$. to the nearest whole unit, what is the length of $overline{cd}$?
a. 26
b. 29
c. 24
d. 21

Explanation:

Step1: Identify right triangles

△ABC and △BCD are right-angled at C.

Step2: Find BC using △ABC

In △ABC, ∠BAC=37°, AC=53. tan(37°)=BC/AC → BC=53×tan(37°)≈53×0.7536≈40.

Step3: Apply geometric mean theorem

△ABD right-angled at B (altitude BC to hypotenuse AD). BC²=AC×CD → CD=BC²/AC≈40²/53≈1600/53≈30.19≈30, nearest to 29.

Answer:

B. 29