Final answer:
To solve the triangle using the Law of Sines, we can follow these steps: Draw the triangle based on the given information, label the triangle, and use the Law of Sines to find the missing side and angles. In this case, we are given angle A, angle C, and side b. By plugging in the values and using the Law of Sines formula, we can find the missing side of the triangle.
Step-by-step explanation:
To solve the triangle using the Law of Sines, we can start by drawing the triangle based on the given information. We are given that angle A is 30 degrees, angle C is 65 degrees, and side b is 10 units long. Let's label the triangle accordingly. Now, we can use the Law of Sines to find the missing side and angles.
The Law of Sines states that a/sin(A) = b/sin(B) = c/sin(C), where a, b, and c are the lengths of the sides opposite to angles A, B, and C respectively. In our case, we are given side b, angle A, and angle C. We can use the Law of Sines to find side a, which is opposite to angle A.
We can rearrange the formula to solve for side a: a = b * (sin(A) / sin(B)). Plugging in the given values, we have a = 10 * (sin(30) / sin(65)). Using any scientific calculator, we can evaluate this expression to get the exact value of side a. So, using the Law of Sines, we have found the missing side of the triangle.