Answer:
51.34
Step-by-step explanation:
First, things first, identify the opposite, adjacent, and hypotenuse.
Since you are trying to find the value of x, the length measuring 4 is the adjacent because it is one of the lengths that creates that angle measure you are trying to find. 5 is the opposite because the angle is on the opposite side of the length. The [tex]\sqrt{41}[/tex] is the hypotenuse.
Now, which trig equation do you want to use?
sin(x) = opposite / hypotenuse
cos(x) = adjacent / hypotenuse
tan(x) = opposite / adjacent
Let's first try solving with sine.
sin(x) = 5/[tex]\sqrt{41}[/tex]
Since you want to find the angle, you have to use the [tex]sin^{-1} (\frac{5}{\sqrt{41}} )=x[/tex]
Plug it into your calculator, then you should get something like this: 51.34019175.
That is the angle measurement of x.
Let's use cosine.
cos(x) = 4/[tex]\sqrt{41}[/tex]
Again, since you want to find the angle, you have to use the [tex]cos^{-1} (\frac{4}{\sqrt{41}} )=x[/tex]
Plug it into your calculator, then you should get something like this: 51.34019175.
You realize that it gave the same answer, right? Yep, let's also do tangent.
tan(x) = 5/4
Again, since you want to find the angle, you have to use the [tex]tan^{-1}(\frac{5}{4}} )=x[/tex]
Type it into the calculator and you should get 51.34019175 again!
