Answer :
Final answer:
To solve for the remaining sides and angles in the triangle, we can use the Law of Sines. Given side length b = 5, angle y = 170°, and side length c = 98.3, we can calculate angle B ≈ 3.74°, angle C ≈ 6.26°, and side a ≈ 5.97 units using the Law of Sines.
Explanation:
To solve for the remaining sides and angles in this triangle, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles in a triangle. We are given side length b = 5, angle y = 170°, and side length c = 98.3. To find angle B, we can use the sine rule: sin(B)/b = sin(Y)/y. Rearranging the equation, we have sin(B) = (b * sin(Y))/y. Substituting the given values, we have sin(B) = (5 * sin(170))/170. Using a calculator, we find sin(B) ≈ 0.0653. Taking the inverse sine of sin(B), we find angle B ≈ 3.74°. To find angle C, we can use the fact that the sum of the angles in a triangle is 180°. Angle C = 180° - angle B - angle Y = 180° - 3.74° - 170° ≈ 6.26°. To find side a, we can use the sine rule again: sin(A)/a = sin(Y)/y. Rearranging the equation, we have sin(A) = (a * sin(Y))/y. We can substitute the values of angle Y and side length c to find sin(A): sin(A) = (a * sin(170))/98.3. Solving for a, we have a = (sin(A) * 98.3)/sin(170). Plugging the given values into the equation, we find that a ≈ 5.97. Therefore, the value of side a is approximately 5.97 units.
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