Question

question 5 of 5
type the correct answer in the box. use numerals instead of words.
what is dc to the nearest tenth?
dc =

Explanation:

Step1: Use Pythagorean theorem in right - triangle AEC

In right - triangle AEC, if $AE = 15$ and $AC = 22$, by the Pythagorean theorem $EC=\sqrt{AC^{2}-AE^{2}}$.
$EC=\sqrt{22^{2}-15^{2}}=\sqrt{(22 + 15)(22 - 15)}=\sqrt{37\times7}=\sqrt{259}\approx16.1$.

Step2: Use Pythagorean theorem in right - triangle DEC

In right - triangle DEC, if $DE = 28$ and $EC\approx16.1$, by the Pythagorean theorem $DC=\sqrt{DE^{2}+EC^{2}}$.
$DC=\sqrt{28^{2}+16.1^{2}}=\sqrt{784 + 259.21}=\sqrt{1043.21}\approx32.3$.

Answer:

$32.3$