Answer:
33,2 ≈ c
45 ≈ b
120° = A
Step-by-step explanation:
We will be using the Law of Sines:
Solving for Angle Measures
[tex] \frac{ \sin∠C}{c} = \frac{ \sin∠B }{b} = \frac{ \sin∠A}{a} [/tex]
** In the end, use the sin⁻¹ function or else you will throw off your answer.
Solving for Sides
[tex] \frac{c}{ \sin∠C} = \frac{b}{ \sin∠B} = \frac{a}{ \sin∠A} [/tex]
Given instructions:
Well, the first thing we can do is to find the m∠A, and we have to use the Triangular Interior Angles Theorem:
25° + 35° + m∠A = 180°
|________|
60° + m∠A = 180°
-60° - 60°
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m∠A = 120°
Now that we have the third angle measure, we can use it in the formula to find the other sides of the triangle, like side c:
[tex] \frac{c}{ \sin 25°} = \frac{68}{ \sin 120°} \\ \\ \frac{68 \sin 25°}{ \sin 120°} ≈ 33,18383234 ≈ 33,2 \\ \\ 33,2 ≈ c[/tex]
Now, we have to find side b:
[tex] \frac{b}{ \sin 35°} = \frac{68}{ \sin 120°} \\ \\ \frac{68 \sin 35° }{ \sin 120° } ≈ 45,03701335 ≈ 45 \\ \\ 45 ≈ b[/tex]
Now everything has been defined!
I am joyous to assist you anytime.
