Trig functions, solve for z in triangle

[whitecanvas]

Hi there,

I'm an independent-study student and the textbook I'm studying from is very... :x I'm currently working on trigonometric functions and come across this problem. I am asked to find z of the right triangle, given one size of the triangle as 23, a 39 degree angle. I found the other two angles, 90 and 51, but how do I find the length. Here's a picture:

Can you help me, step-by-step, on how to get the answer? I just know it relates to the sin, cos, tan, etc... but I have no idea where to begin. Thank you very much for any help.

 

[Loren]

In a right triangle, the cosine of an acute angle is defined as the measure of the adjacent side divided by the measure of the hypotenuse...that is \(\displaystyle \sin x = \frac{adj}{hyp}\). In your case \(\displaystyle \sin 39 = \frac{23}{z}\)... solve for z.

Typo has been corrected.

 

[TchrWill]

Hi there,

I'm an independent-study student and the textbook I'm studying from is very... :x I'm currently working on trigonometric functions and come across this problem. I am asked to find z of the right triangle, given one size of the triangle as 23, a 39 degree angle. I found the other two angles, 90 and 51, but how do I find the length. Here's a picture:

Can you help me, step-by-step, on how to get the answer? I just know it relates to the sin, cos, tan, etc... but I have no idea where to begin. Thank you very much for any help.

A
*
*...*
*......*
*.........*
*.............*
C*****************B
Angle ABC = 39º
BC = 23
cos/_ABC = adj/hyp = BC/AB
Therefore, AB = BC/cos(ABC) = 23/.777145 = 29.595

 

[mmm4444bot]

In a right triangle, the sine of an acute angle is defined as the measure of the adjacent side divided by the measure of the hypotenuse...that is \(\displaystyle \sin x = \frac{adj}{hyp}\). In your case \(\displaystyle \sin 39 = \frac{23}{z}\)... solve for z.

Loren is correct, except for the unintentional error with the name of the trigonometric function. Loren meant to type "the cosine of an acute angle", "cos(x)", and "cos(39°)".

sin(angle) = opposite/hypotenuse

cos(angle) = adjacent/hypotenuse

'

… the textbook I'm studying from is very …

… I have no idea where to begin …

If you think this textbook is the issue, why do you continue using it? Perhaps, you should look for a better textbook.

You could also try Google. There are thousands of mathematical lessons and examples on-line. You might even find THIS ONE.

 

[whitecanvas]

Hi there,

Thank you for your replies. I think I'm understanding it now.. I can even use sin with the 51-degree to solve for z too.

^ I have no money for another textbook. Kidding. I'm studying via IS, so whatever book they tell me to get, I get.I checked amazon and there were so many bad reviews on this book... now I see why. Google is my friend.. lol, that's the main reason why I was able to pass my previous math classes as an is student..

Again, thanks everyone for your reply and help. I really, really appreciate it. =]