Question

(20pts)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

To find the answer,we need to first find angle F:

180° = 90°+49°+<F
<F = 180°-49°-90°
<F = 41°

We can then use the sine formula to find x,which is:

$\frac{side \: a}{sin angle \: a} = \frac{side \: b}{sin \: angle \: b}$

In this case

$\frac{55}{sin41} = \frac{x}{sin49} \\ x = \frac{55}{sin41} \times sin49 \\ x = 63.270... \\ x = 63$

Therefore, the answer is 63.

Hope it helps!

Answer 2

Answer: 63.27

Step-by-step explanation:

In trigonometry , if we have a right triangle , then the ratio of the side opposite to an angle and the side adjacent to angle is the tangent of that angle.

From the given figure , we have a right triangle with

Side adjacent to the angle 49°=55 units

the sides opposite to angle  = x

Then by trigonometry , we have

$\tan {49^{\circ}}=\dfrac{x}{55}\\\\\Rightarrow\ x=55\tan(49^{\circ})\\\\\Rightarrow\ x=55\times1.15036840722\\\\\Rightarrow\ x=63.2702623971\approx63.27$

Hence, the value of x = 63.27