Question 1151223: Solve the right triangle. Give angles in degrees and minutes.
A=33.3◦; C=90◦; a=leg; b=3.8m; c=hypotenuse. Round side lengths to one decimal place.
1) B=56.7◦; a=2.5mc = 4.5m
2) B=56.7◦; a=5.0mc = 6.3m
3) B=56.7◦; a=1.4mc = 4.0m
4) B=56.7◦; a=1.4mc = 5.0m
NOTE: can you please tell me which one is the right choice, and how did you get that choice?
NOTE: can you please explain what is (mc) and how to convert it to (m).
Thanks
Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52879)   (Show Source):
You can put this solution on YOUR website! .
Let me explain you about "mc".
Consider, for example, this line from your post
1) B=56.7◦; a=2.5mc = 4.5m
It is written INCORRECTLY in your post, which makes you confused.
The correct writing if THIS :
1) B=56.7◦; a=2.5m, c = 4.5m
with the comma and blank space as dividers between "m" and "c".
And there is NO NEED in any conversion . . .
Is everything clear to you now, related to your NOTE question #2 ?
Thanks for asking . . .
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website!
Refer to this diagram
The side lengths are lowercase letters a,b,c.
The angles are uppercase letters A,B,C.
Note how lowercase a is opposite uppercase A, b is opposite B, c is opposite C. This helps us easily keep track of the values.
What we know so far is...
sides:
a = unknown
b = 3.8
c = unknown
and we also know that,
Angles:
A = 33.3 degrees
B = unknown
C = 90 degrees
Use the fact that A+B+C = 180 to solve for B
A+B+C = 180
33.3+B+90 = 180
B+123.3 = 180
B+123.3-123.3 = 180-123.3
B = 56.7 degrees
Then use the tangent rule to find the length of side a.
tan(angle) = opposite/adjacent
tan(A) = a/b
tan(33.3) = a/3.8
3.8*tan(33.3) = a
a = 3.8*tan(33.3)
a = 2.49613344512487
a = 2.5
Make sure your calculator is in degree mode.
We could now use either sine or cosine to find the hypotenuse
sin(angle) = opposite/hypotenuse
sin(A) = a/c
sin(33.3) = 2.49613344512487/c
c*sin(33.3) = 2.49613344512487
c = 2.49613344512487/sin(33.3)
c = 4.54650219134128
c = 4.5
Or,
cos(angle) = adjacent/hypotenuse
cos(A) = b/c
cos(33.3) = 3.8/c
c*cos(33.3) = 3.8
c = 3.8/cos(33.3)
c = 4.54650219134128
c = 4.5
Or yet another way is to use the pythagorean theorem
a^2 + b^2 = c^2
2.49613344512487^2 + 3.8^2 = c^2
6.23068217587096 + 14.44 = c^2
20.670682175871 = c^2
c^2 = 20.670682175871
c = sqrt(20.670682175871)
c = 4.54650219134128
c = 4.5
Either way we get the same approximate value for c.
--------------------------------------------------
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Summary:
The fully solved triangle ABC has the following properties
sides:
a = 2.5
b = 3.8
c = 4.5
Angles:
A = 33.3 degrees
B = 56.7 degrees
C = 90 degrees
The values in red are the answers we found earlier.
Diagram:
We can see that the final answer is Choice 1) B = 56.7 degrees; a = 2.5 m, c = 4.5 m
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