Suppose you are presented with a triangle and given two of its sides with an included angle measure. Place in order the reasonable steps you would use to solve the triangle (1 is the first step and 3 is the last)

Question 1 options:

__Use Law of Sines to find the one missing side.

__Use the Law of Cosines to find one of the missing angles.

__Subtract from 180˚ to find the missing angle measure.

Answer: The correct order is;

Step 2, Step 1 and Step 3

Step-by-step explanation: In solving for a triangle, the sine rule and the cosine rule can be applied as far as certain conditions exist or are met in the question. The sine rule is given as

a/SinA = b/SinB = c/SinC

In order to use the sine rule, at least one side and two angles, OR at least one angle and two sides must be given. Where you are given two sides and one angle (like in the question above), the given angle must be opposite one of the sides given. Since the question does not specify that the given angle is opposite any of the two given sides, then we can safely assume that it is opposite the third side which is unknown. Based on that assumption, we shall start with the Cosine rule which is given as

a² = b² + c² - 2bcCosA

Where a is the unknown side and A is the given angle facing the unknown side a.

With sides a, b and c now known, we can apply the sine rule to calculate for one of the other unknown angles. Remember that having three sides and one angle satisfies the condition for applying the sine rule. Since side a and angle A are now available, we can calculate one of the other angles as follows;

a/SinA = b/SinB

With this we can now derive the size of angle B. Having found angle A and angle B, we simply subtract the addition of both angles from 180° in order to derive the third angle.