Question 1204365: Assume 𝛼 is opposite side a, 𝛽 is opposite side b, and 𝛾 is opposite side c. Solve the triangle, if possible. Round your answers to the nearest tenth. (If not possible, enter IMPOSSIBLE.)
b = 9, 𝛽 = 98°, 𝛾 = 30°
Found 2 solutions by Theo, math_tutor2020:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i will use 𝛼 = angle A, 𝛽 = angle B, 𝛾 = angle C, a = side a, b = side b, c = sice c, because it's easier to type the problem and solution that way.
you are given that:
sside b = 9, angle B = 98 degrees, angle C = 30 degrees.
the triangle is solved as shown below.
angle A = 52 degrees
angle B = 98 degrees
angle C = 30 degrees
side a = 7.161794878 (shown as y in the diagram).
side b = 9 (showon as 9 in the diagram).
side c = 4.544224076 (shown as x in the diagram).
i used the law of sines to folve.
law of sines states that sin(A) / a = sin(B) / b = sin(C) / c
round your answers as required.
here's my diagram.
note:
angle A was equal to 52 degrees because the sum of the interior angles of a triangle = 180.
Answer by math_tutor2020(3817)  (Show Source):
You can put this solution on YOUR website!
𝛼 = Greek letter alpha (lowercase)
𝛽 = Greek letter beta (lowercase)
𝛾 = Greek letter gamma (lowercase)
𝛼 = unknown for now
𝛽 = 98°
𝛾 = 30°
𝛼 + 𝛽 + 𝛾 = 180
𝛼 + 98 + 30 = 180
𝛼 + 128 = 180
𝛼 = 180-128
𝛼 = 52
Sides
a = unknown
b = 9
c = unknown
Angles
𝛼 = 52°
𝛽 = 98°
𝛾 = 30°
Law of Sines
sin(𝛼)/a = sin(𝛽)/b
sin(52)/a = sin(98)/9
9*sin(52) = a*sin(98)
a = 9*sin(52)/sin(98)
a = 7.16179487789919 approximately
a = 7.2
Please make sure your calculator is set to degree mode.
Also,
sin(𝛽)/b = sin(𝛾)/c
sin(98)/9 = sin(30)/c
c*sin(98) = 9*sin(30)
c = 9*sin(30)/sin(98)
c = 4.54422407633379 approximately
c = 4.5
The fully solved triangle has these angles and sides:
| Angles | Sides | 𝛼 = 52°
𝛽 = 98°
𝛾 = 30° | a = 7.2 approximately
b = 9
c = 4.5 approximately |
Diagram
Only one unique triangle is possible due to the AAS congruence theorem.
More practice
https://www.algebra.com/algebra/homework/Trigonometry-basics/Trigonometry-basics.faq.question.1204286.html
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