Question

Please help!?
Use △DEF, shown below, to answer the question that follows: What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below

Answer 1

Answer:

x=63.25

Step-by-step explanation:

Hi there!

We're given ΔDEF with m<E=90°, m<D=49°, DE=55, and EF=x

we need to find the value of x

Let's use trigonometry to do it

Since we are given the measures of the 2 legs (the sides that make up the 90° angle), let's use tangent, specifically tan(49), since we are given the measure of that angle

Recall that tangent is $\frac{opposite}{adjacent}$

in reference to m<D (the angle that is 49°), the opposite side is EF (x) and the adjacent side is DE (55)

so tan(49)=$\frac{x}{55}$

plug tan(49) into your calculator; remember to have the calculator on degree mode

tan(49)≈1.15 (rounded to the nearest hundredth)

so that means:

1.15=$\frac{x}{55}$

multiply both sides by 55 to clear the fraction

63.25=x

Hope this helps!