In the diagram below, BC is an altitude of ABD. To the nearest whole unit, what is the length of CD?

First we need to calculate the 2 angles that make up Angle B at the top of the triangle.
Using that angle we can find the length of CD.

See the attached picture:

Answer Link

ApusApus ApusApus · Answer 2 · 2019-07-03T13:33:40+02:00

Answer:

D. 26.

Step-by-step explanation:

We have been given an image of a triangle. We are asked to find the length of CD.

We will use altitude on hypotenuse theorem to solve our given problem.

[tex]\frac{CD}{\text{Altitude}}=\frac{\text{Altitude}}{AC}[/tex]

Upon substituting our given values, we will get:

[tex]\frac{CD}{37}=\frac{37}{53}[/tex]

[tex]\frac{CD}{37}\times 37=\frac{37}{53}\times 37[/tex]

[tex]CD=\frac{37\times 37}{53}[/tex]

[tex]CD=\frac{1369}{53}[/tex]

[tex]CD=25.830188679\approx 26[/tex]

Therefore, the length of CD is 26 units and option D is the correct choice.