Question

type the correct answer in the box. use numerals instead of words.
what is $dc$ to the nearest tenth?
$dc = \square$

Explanation:

Step1: Find length of BC

First, use the Pythagorean theorem in right triangle ABC to find BC.
$$BC = \sqrt{AC^2 - AB^2} = \sqrt{22^2 - 15^2}$$
$$BC = \sqrt{484 - 225} = \sqrt{259} \approx 16.09$$

Step2: Find length of DC

Use the Pythagorean theorem in right triangle DBC to find DC.
$$DC = \sqrt{DB^2 + BC^2} = \sqrt{28^2 + (\sqrt{259})^2}$$
$$DC = \sqrt{784 + 259} = \sqrt{1043} \approx 32.3$$

Answer:

32.3