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Find the value of x in the triangle. Round your answer to the nearest tenth of a degree. Show your work.

This is what I have so far...

In this problem we are trying to find the degree for the angle ‘x’.

Because the triangle is a right triangle and we are using the ‘x’ angle to work with we know that 14.6 units is the opposite side and 7.2 units is the adjacent.

Using the Trigonometric equation we can find the degree of the angle ‘x’.

\(Tan(x)= \frac{opposite}{adjacent}\)

Substitute the known values…

\(Tan(x)=\frac{14.6}{7.2}\)

But then I don't know how to get

xº=Tan^-1 (14.6/7.2)

Like wouldn't it be dividing? and then what do you do? How does that get to 63.7º? What do you have to do to the Tan^-1 to get to that? I think whats really throwing me off is the ^-1.

Im so sorry please help me!!

Whoever answers this, I have one other question that I'm about to post if you could look at that one too it would be a great help!

KennedyPape Dec 15, 2018

#1**+3 **

You're on the right track....just a calculator problem....

On the home page calculator....make sure you're in * DEGREE* Mode....[at bottom left ]

Key in

14.6 / 7.2

Then....hit the "2nd button"

You will see the "atan" button....hit that

Then hit "="

You should see "63.749....."

This where "63.7" comes from.....

Hope that helps.....incidentally..."atan" is the same as "tan^{-1} ".....it means "tangent inverse"

CPhill Dec 15, 2018

#2**+3 **

How did you get the x alone? by subtracting, adding, multipling, or dividing tan on both sides? And by doing that it gets you the inverse of Tan which is Tan^-1?

* Thank you for helping me, Ik it's super late.

KennedyPape
Dec 15, 2018

#3**+3 **

OK....I know this is confusing [ don't worry..I'm a "night owl"...LOL!!!]

Note

Tan x = 14.6/ 7.2

This tells us the ratio of the opposite /adjacent sides to the angle , x

The inverse actually tells us what x is [ the angle measure of x]

So

atan (14.6/ 7.2] = x = 63.7

Remember....the trig function tells us a ratio ......the inverse returns the angle value of that ratio

CPhill
Dec 15, 2018