Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 months ago

# solve right triangle ABC with C the right angle if angle B=56.4 degrees and side c=12.3 Round to the nearest tenth.?

This is one of my final review questions but i do not have a answer key! Just trying to check my work.

I got

Angle A= 33.6

Side a= 6.8

Side b= 10.3

Please provide proof that i am wrong or right

I do not need a simple yes or no! Thanks so much

Relevance

The sum of the three angles in a triangle will always be 180°.  We have two of the three so we can solve for the third:

A + B + C = 180

A + 56.4 + 90 = 180

A + 146.4 = 180

A = 33.6°

Now that we have that we can use the known angles and one known length and the law of sines to solve for the other two unknown lengths:

a / sin(A) = c / sin(C) and b / sin(B) = c / sin(C)

a / sin(33.6) = 12.3 / sin(90) and b / sin(56.4) = 12.3 / sin(90)

a / sin(33.6) = 12.3 / 1 and b / sin(56.4) = 12.3 / 1

a / sin(33.6) = 12.3 and b / sin(56.4) = 12.3

a = 12.3 sin(33.6) and b = 12.3 sin(56.4)

a = 6.8 and b = 10.2

So other than you not including the label in your angle answer and a little rounding error in your "b", you have the correct answers.

• ACB is a right triangle

in which Angle C = 90°, Angle B = 56.4° and c = 12.3

Angle A = 33.6°

Sides: c = 12.3   b = 10.245   a = 6.807

• m∠A = 180 - (m∠B + m∠C) = 180 - (56.4° + 90°) = 33.6°

∠C is right angle so side c is hypotenuse

sinA = a/c

a = csinA = 12.3 sin33.6 = 6.8

sinB = b/c

b = csinB = 12.3 sin56.4 = 10.2

• a = 12.3 sin 33.6°= 6.81 , b = 12.3 sin 56.4 = 10.24...so good work
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