# Right triangle in trig

Hi, I am having trouble with this problem. My Geometry text book explains how to do this, but not very well, and I have come to a problem on a practice test that is nothing like what's in the book. I would really appriciate some help with this please!

*Figure is a right triangle

Question: Given the Figure below (right triangle), find ,
a if sin B = 0.42, cos B = 0.91, tan B = 0.47 and c =60

Thank you very very much!

#### kompik

Hi, I am having trouble with this problem. My Geometry text book explains how to do this, but not very well, and I have come to a problem on a practice test that is nothing like what's in the book. I would really appreciate some help with this please!

*Figure is a right triangle

Question: Given the Figure below (right triangle), find ,
a if sin B = 0.42, cos B = 0.91, tan B = 0.47 and c =60

Thank you very very much!
Since you know the value of sin B and c, you could simply use the equation
sin B=b/c
to calculate b and then plug this into Pythagorean theorem
a^2+b^2=c^2
to get a.

But even simpler: If you know that in right triangle sin A=cos B, then you have
cos B=sin A=a/c
from which you can easily get a.

(I guess that A is the angle opposite to the side a and B is the angle opposite to the side b - this is probably shown in the figure you did not show us. Am I right?)

#### earboth

MHF Hall of Honor
Hi, I am having trouble with this problem. My Geometry text book explains how to do this, but not very well, and I have come to a problem on a practice test that is nothing like what's in the book. I would really appriciate some help with this please!

*Figure is a right triangle

Question: Given the Figure below (right triangle), find ,
a if sin B = 0.42, cos B = 0.91, tan B = 0.47 and c =60

Thank you very very much!
1. Use the definition of the trigonometric functions in a right triangle:

$$\displaystyle \sin(B)=\frac bc$$

$$\displaystyle \cos(B)=\frac ac$$

$$\displaystyle \tan(B)=\frac ba$$

2. Choose the appropriate equation to calculate a.

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Ok, I found a figure online similar to the figure I am trying to solve. It's the same thing it's just flipped the opposite way.

So, would I be doing the same thing that you told me to do?

*figure in my book is flipped so A is facing the right.

Thank you!