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…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter5: Similar Triangles

Section5.CT: Test

Problem 6CT: In right triangle ABC,CD- is the altitude from C to hypotenuse AB-. Name three triangles that are...

See similar textbooks

Related questions

Question

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 $= 180^{\circ}$

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

Step by step

Solved in 3 steps

Knowledge Booster

$Basics (types, similarity, etc)$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions