explain how you would solve a triangle given two sides and the included angle
To solve a triangle given two sides and the included angle, you can use the Law of Cosines. This law states that the square of one side of a triangle is equal to the sum of the squares of the other two sides, minus twice the product of those sides and the cosine of the included angle.
Here's how you can solve the triangle:
1. Label the triangle with the given sides and angle. Let's say side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C (the included angle).
2. Use the Law of Cosines to find the unknown side. For example, if you want to find side c, use the formula c^2 = a^2 + b^2 - 2ab cos(C).
3. Solve for the unknown side by taking the square root of the result from step 2.
4. Use the Law of Sines to find the other angles of the triangle. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides.
5. Finally, use the fact that the angles of a triangle sum up to 180 degrees to find the third angle of the triangle.
By following these steps, you can solve a triangle given two sides and the included angle.
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To solve a triangle when you know two sides and the angle between them, you can use the Law of Cosines. This law helps you find the length of the missing side by using the lengths of the known sides and the cosine of the included angle.
Here's how you can do it:
1. Identify the triangle's sides and angles. Let's call the sides a, b, and c, and the angles A, B, and C, with C being the included angle.
2. Use the Law of Cosines formula c^2 = a^2 + b^2 - 2ab * cos(C) to find the length of the missing side.
3. After finding the length of the missing side, take the square root of this value to get the actual length.
4. Next, use the Law of Sines to find the other angles of the triangle. This law helps you relate the lengths of the sides to the sine of their opposite angles.
5. Finally, remember that the angles of a triangle always add up to 180 degrees. Use this fact to find the third angle of the triangle.
By following these steps, you can confidently solve a triangle given two sides and the included angle.
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Sure thing!
First, we need to use the Law of Cosines to find the missing side of the triangle. The formula for this is c^2 = a^2 + b^2 - 2ab * cos(C), where a and b are the lengths of the known sides and C is the included angle.
Once we solve for the missing side length, we take the square root of that value to get the exact length.
Next, we apply the Law of Sines to find the other two angles of the triangle. This law helps us relate the lengths of the sides to the sines of their opposite angles.
Lastly, remember that the interior angles of a triangle always add up to 180 degrees. Using this, we can figure out the measure of the third angle in the triangle.
By following these steps, you can successfully solve a triangle when given two sides and the included angle.