Question

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

Triangle DEF where angle E is a right angle. DE measures x. DF measures 55. Angle F measures 49 degrees.
What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.


Please explain your answer.

Answer 1

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 = \frac{\textrm{opp}}{\textrm{hyp}} = (DE)/(DF)`

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

Answer: 49.51

Answer 2

DE= 3.75 units

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 = (perpendicular)/(Hypotenuse)`

Perpendicular = DE

Hypotenuse = DF = 55

`\theta=49` Degrees

`sin 49= (DE)/(55)`

We use trigonometric calculator and find sin 49° = 0.75

Hence we have

`0.75= (DE)/(55)`

DE= 55*0.75

DE=41.509 units