Question

Problem is attached, need to use sin and cosine formulas

Answer 1

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.

What is the law of sines?

For any triangle ABC, with side measures |BC| = a. |AC| = b. |AB| = c,

we have, by law of sines,

$\dfrac{\sin \alpha }{a} = \dfrac{\sin \beta }{b} = \dfrac{\sin \gamma}{c}$

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°.

$\dfrac{\sin 65^o}{a} = \dfrac{\sin 15^o}{12} = \dfrac{\sin 100^o}{c}$

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:

https://brainly.com/question/17289163

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