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

Triangle DEF where angle E is a right angle. DE measures 55. EF measures x. Angle D measures 49 degrees.

What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.

Question

Use △DEF, shown below, to answer the question that follows: 

Triangle DEF where angle E is a right angle. DE measures 55. EF measures x. Angle D measures 49 degrees. 

What is the value of x rounded to the nearest hundredth? Type the numeric answer only in the box below.

jonathan5824 · Answer

https://lh3.googleusercontent.com/tzxk01dsYFXW97n6f9iJgb0z1PMWyYoa23PQayaLwj6ogYO3y32ghJD8p3Bvzuhd823-=s141

scooby6363 · Answer

Hint - You will be using tangent and the angle of 49 degrees instead of the angle of 90 degrees.

Do you understand what to do next?

jonathan5824 · Answer

Well i got 36.08 but it said it was wrong can you explain why

jonathan5824 · Answer

would it be 35.46

scooby6363 · Answer

Tangent will only be using the side opposite to the angle and the side adjacent to the angle. We will be focusing on the angle of 49 degrees since you cannot use sin, cosine, or tangent to measure the sides with the right angle.
$$\tan(49degrees) = x/55$$
This will be the equation you are going to want to follow. X is the length of the opposite side while 55 is the length of the adjacent side. All you need to do is solve for X by multiplying both sides by 5. You are going to be required to use a calculator in order to find the values when using these trigonometric functions.
$$\tan(49 degrees)*55 = 63.27$$
So 63.27 is equal to X. This can be checked by doing:
$$\tan^{-1} (63.27/55) = 49 degrees$$
Do you understand now? I do not want to confuse you with this.

jonathan5824 · Answer

Thank you I understand completely! I see where I messed up so X=63.27