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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,
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°.
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:
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For this, we will be using the quadratic formula, which is , with a=x^2 coefficient, b=x coefficient, and c = constant. Our equation will look like this:
Firstly, solve the multiplications and the exponents:
Next, do the addition:
Next, your equation will be split into two: . Solve them separately, and your answer will be