In triangle 1, the values are α = 65°, a = 42.02, and 45.66. And in triangle 2, the values are β = 55.74, γ = 84.26, and c = 10.84.
<h3>What is the law of sines?</h3>
For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,
we have, by law of sines,
![\dfrac{\sin \alpha }{a} = \dfrac{\sin \beta }{b} = \dfrac{\sin \gamma}{c}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%20%5Calpha%20%7D%7Ba%7D%20%3D%20%5Cdfrac%7B%5Csin%20%5Cbeta%20%7D%7Bb%7D%20%3D%20%5Cdfrac%7B%5Csin%20%5Cgamma%7D%7Bc%7D)
1. β = 15°, γ = 100°, and b = 12, then the missing side and angle will be
The sum is 180° of a triangle. Then the value of α will be 65°.
![\dfrac{\sin 65^o}{a} = \dfrac{\sin 15^o}{12} = \dfrac{\sin 100^o}{c}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csin%2065%5Eo%7D%7Ba%7D%20%3D%20%5Cdfrac%7B%5Csin%2015%5Eo%7D%7B12%7D%20%3D%20%5Cdfrac%7B%5Csin%20100%5Eo%7D%7Bc%7D)
Then the value of a will be
a = 42.02
Then the value of c will be
c = 45.66
2. α = 40°, a = 7, and b = 9, then the missing side and angle will be
(sin 40°)/7 = (sin β) / 9
sin β = 0.82644
β = 55.74
The sum is 180° of a triangle. Then the value of γ will be 84.26°.
Then the value of c will be
c = 10.84
Learn more about the law of sines here:
brainly.com/question/17289163
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