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:


`(side \: a)/(sin angle \: a) = (side \: b)/(sin \: angle \: b)`

In this case


`(55)/(sin41) = (x)/(sin49) \\ x = (55)/(sin41) * sin49 \\ x = 63.270... \\ x = 63`

Therefore, the answer is 63.

Hope it helps!

Answer 2

Answer: 63.27

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)}=(x)/(55)\\\\\Rightarrow\ x=55\tan(49^(\circ))\\\\\Rightarrow\ x=55*1.15036840722\\\\\Rightarrow\ x=63.2702623971\approx63.27`

Hence, the value of x = 63.27