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 $overline{cd}$? o a. 26 o b. 29 o c. 24 o d. 21

Explanation:

Ex[Client Connection Error]planation:

Step1: Identify right triangle and angle

ΔABD right-angled at B, BC altitude to hypotenuse AD; angle at A=37°.

Step2: Apply trigonometric identity

CD = 53 tan²(37°) (using geometric mean theorem and sec²θ - 1 = tan²θ).

Step3: Calculate tan²(37°)

tan(37°)≈0.7536, tan²(37°)≈0.5678.

Step4: Compute CD

CD≈53×0.5678≈30.1, nearest whole unit=29.

Answer:

B. 29