Question

Find the value of m, rounded to the nearest tenth.

Screenshot below.
Will fan and medal!!
Tanks!

Answer 1

A. 13.6
B. 27.0
C. 32.3
D. 38.6

Answer 2

do you know the acronym SOHCAHTOA?

If you have a right triangle, with the longest side known as the hypotenuse, you can work out the sides and angles from SOHCAHTOA:

SOH: sine = opposite / hypotenuse
CAH: cosine = adjacent / hypotenuse
TOA: tangent = opposite / adjacent

Answer 3

Looking at your diagram, you know the length of the side adjacent to the angle, you know the angle, and you wish to know the length of the hypotenuse. Which of SOH CAH TOA contains those three items?

Answer 4

Yes, I started using CAH.

I did cos 39 = \[\left(\begin{matrix}21 \\ m\end{matrix}\right)\]

Answer 5

then I multiplied 21 on each side...

Answer 6

okay,
\[\cos 39^\circ = \frac{21}{m}\]Now we need to solve that equation for \(m\) and evaluate it.

Answer 7

I think you need to multiply both sides by \(m\) and divide both sides by \(\cos 39^\circ\)

Answer 8

?? Okay. So it would look more like this...

\[m * \cos39 = \left(\begin{matrix}21 \\ m\end{matrix}\right) * m\] ?

Answer 9

Look, if you have this equation:

\[a = \frac{b}{c}\]and you want to solve for \(c\):

\[a*c = \frac{b*c}{c}\]\[ac = b\]\[\frac{ac}{a} = \frac{b}{a}\]\[c = \frac{b}{a}\]right?

Answer 10

right.

Answer 11

That is what we are doing here.

\[\cos 39^\circ = \frac{21}{m}\]multiply both sides by \(m\):\[m \cos 39^\circ = m \frac{21}{m}\] \[m \cos 39 ^\circ = 21\]now divide both sides by \(\cos 39^\circ\)

Answer 12

OH!! Ok, that makes since now.

so m = 27.0 right?

Answer 13

Yes!

(sense, btw)

Answer 14

THANK YOU SO MUCH!!

Answer 15

U r a lifesaver!!

Answer 16

Eh, you see a few of these worked out and you'll wonder why it ever stumped you...glad I could help!

Answer 17

XD