Solve the triangle, if possibleA = 30 degreeB= ? degreeC=? degreea =b= 23C=8Select the correct choice below and, if necessary, fill in the answer boxes to complete yourchoice. (Round side lengths to the nearest whole number and angle measures to the nearestdegree as needed.)

Answered: Solve the triangle, if possible A= 30…

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter61: Areas Of Circles, Sectors, And Segments

Section: Chapter Questions

Problem 38A: Three pieces, each in the shape of a sector, are cut from the rectangular sheet of steel shown. How...

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Solve the triangle, if possible
A = 30 degree
B= ? degree
C=? degree
a =
b= 23
C=8
Select the correct choice below and, if necessary, fill in the answer boxes to complete your
choice. (Round side lengths to the nearest whole number and angle measures to the nearest
degree as needed.)

Expert Solution

Step 1

Given,

$A = 30^{\circ}, b = 23, c = 8$

Step 2

Using formula,

$a^{2} = b^{2} + c^{2} - 2 b c \cos A a^{2} = 23^{2} + 8^{2} - 2 (23) (8) \cos 30^{\circ} a^{2} = 529 + 64 - 368 (\frac{\sqrt{3}}{2}) a = 16$

Using the law of sine

$\frac{\sin A}{a} = \frac{\sin B}{b} \frac{\sin 30^{\circ}}{16} = \frac{\sin B}{23} \sin B = \frac{23 \sin 30^{\circ}}{16} \Rightarrow B = \sin^{- 1} (\frac{23 \sin 30^{\circ}}{16}) \Rightarrow B = 46^{\circ}$

And

Sum of the angle of the triangle $= 180^{\circ}$

$\Rightarrow A + B + C = 180^{\circ} \Rightarrow 30^{\circ} + 46^{\circ} + C = 180^{\circ} \Rightarrow 76^{\circ} + C = 180^{\circ} \Rightarrow C = 180^{\circ} - 76^{\circ} \Rightarrow C = 104^{\circ}$

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