Question

Look at the figure below:

Triangle ABC is a right triangle with angle ABC equal to 90 degrees. The length of AC is 6 units, and the length of AB is 5 units. D is a point above C. Triangle ADC is a right triangle with angle DAC equal to 90 degrees and DC parallel to AB.

What is the length, in units, of segment CD?

11
7.2
5.5
10

Answer 1

Answer:

7.2

took the test

Step-by-step explanation:

Answer 2

The length of segment CD is 7.2

hence option 2 is correct

From the given figure we can  write down the given data

AB = 5

AC = 6

ΔABC is a right triangle

Also ΔADC is a right triangle

AB || CD

We have to find out the length of CD

$\rm Let\; \angle BAC = \theta$

As AB || CD

$\rm \angle ACD = \theta$

$\rm writing \; \cos\theta \; for\; triangle \; ABC \; and\; triangle \; ACD$

$\rm cos\; \theta = \dfrac{5}{6}= \dfrac{6}{CD} \\\\solving\; for \; CD \; gives\; us\\\\CD =7.2$

The length of segment CD is 7.2

hence option 2 is correct

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