Question

Find the measure of angle x. Round your answer to the nearest hundredth. (please type the numerical answer only)

Answer 1

hmm, which class is this for?

Answer 2

Geometry

Answer 3

So lets see, have you used trig before? like sin, cos?

Answer 4

a little bit

Answer 5

Okay good, that makes it easier then...and it's very easy I'll explain step by step

Answer 6

So we have a triangle

Answer 7

Notice that we have an angle that we want....as well as 2 sides of the triangle known

In reference to the angle...we know the side opposite that angle.....and we also know the side adjacent to the angle...right?

Answer 8

yes

Answer 9

So think back to your trig functions

sine
cosine
tangent

Which one of those uses those sides? the opposite and adjacent?

Answer 10

cosine?

Answer 11

Not quite

There is a VERY easy way to remember which functions require which sides

Remember SOH-CAH-TOA

S sine
O opposite
H hypotenuse
C cosine
A adjacent
H hypotenuse
T tangent
O opposite
A adjacent

So sin = opposite / hypotenuse
cos = adjacent / hypotenuse
tan = opposite / adjacent

Answer 12

Ohh okay

Answer 13

Now I know you're like wtf why would that help? how will I remember that? turn it into a sentence

Like

Some - Old - Horse - Caught - Another - Horse - Tripping - Over - Apples

Haha or something corny like that XD

Answer 14

So now you see that

\[\large \tan(x) = \frac{opposite}{adjacent} = \frac{8}{15}\]

right? now there is only 1 more step

Answer 15

okay, I'm starting to understand

Answer 16

So since we have

\[\large \tan(x) = \frac{8}{15}\]

We need to solve for 'x' *notice we are solving for tan(x) there* how would we solve for just 'x'?

Well if you've noticed...every trig function (sin, cos, tan) also has an inverse function (arcsin, arccos, arctan)

And what we see is that if we take the inverse function, of the function...they cancel

i.e.

\[\large arctan(tan(x)) = x\]

So it seems with our \(\large tan(x) = \frac{8}{15}\) if we just take the arctan of both sides, we can solve for 'x'

\[\large x = arctan(\frac{8}{15})\]

Plugging that into any calculator **************in degrees mode****************** will give you your angle :)

Answer 17

so would my answer be 2.128

Answer 18

Not quite

That might be in radians *that's why I tried to emphasize that the calculator has to be in degrees mode before you do the calculation

Because what I get is

\[\large \arctan(\frac{8}{15}) = 28.07 \text{ Degrees}\]

Answer 19

okay, thank you!

Answer 20

No problem! I hope it made sense :)