Question

Use △DEF, shown below, to answer the question that follows:

Answer 1

Answer:

DE= 3.75 units

Step-by-step explanation:

Here we are given a right triangle Δ DEF right angled at E.

We are given that ∠EFD=49°

and DF = 55

DF is our hypotenuse .

Here we have to find the value of DE.

In order to do so , we will use trigonometric ratios

We know that

$sin \theta = \frac{perpendicular}{Hypotenuse}$

Perpendicular = DE

Hypotenuse = DF = 55

$\theta=49$ Degrees

$sin 49= \frac{DE}{55}$

We use trigonometric calculator and find sin 49° = 0.75

Hence we have

$0.75= \frac{DE}{55}$

DE= 55*0.75

DE=41.509 units

Answer 2

We're told E is right and we're given DF, the hypotenuse. We seek x=DE, the side opposite vertex F.

We have opposite and hypotenuse; that's sine.

$\sin F = \dfrac{\textrm{opp}}{\textrm{hyp}} = \dfrac{DE}{DF}$

$x = DE = DF \sin F = 55 \sin 49^\circ = 41.50902...$

Answer: 49.51