Solve each triangle ABC.
A = 68.41°, B = 54.23°, a = 12....

Question

Solve each triangle ABC.

A = 68.41°, B = 54.23°, a = 12.75 ft

Accepted Answer

Hey, everyone here we are asked to find the missing side links and angle of the triangle ABC. Here we are given capital A is equal to 47.82 degrees. Capital B is equal to 72.34 degrees. And lower case A is equal to 11.21 ft. We have four answer choice options, answer choices A through D, each of which state some angle for capital C as well as varying side links for lengths B and C. So to start this problem, we want to find our missing angle capital C. So first we need to recall the angle sum property of a triangle where here for triangle ABC, we have angle capital A plus angle. Capital B plus angle. Capital C is equal to 180 degrees. Now, we just want to substitute in our given information. And so we have 47.82 degrees plus 72.34 degrees plus angle C is equal to 180 degrees. And now we just want to solve four angle C by subtracting the other two angles from both sides of the equation. And in doing so we find that angle, capital C is equal to 59.84 degrees. And now that we have found our missing angle, we can move on to finding our missing side lengths. So for these next steps, we need to recall the law of signs which states that lowercase A divided by sine of capital A is equal to lowercase B divided by S of capital B, which is also equivalent to lowercase C divided by sign of capital C. And now we want to use this a expression from our formula to find our values for lowercase B and lowercase C. So we can start by finding lowercase B. And so just substituting in the values given, we have for lowercase A 11.21 which is divided by S of capital A, which is also given as 47 0.82 degrees. And now, from our law of signs, we know this expression is equivalent to lowercase B divided by S of capital B which is given as 72.34 degrees. And now we just want to solve this equation for lowercase B by just multiplying both sides by a sign of 72.34 degrees. So multiplying and rewriting, we have B lowercase B is equal to 11.21 multiplied by sine of 72.34 degrees, all divided by S of 47.82 degrees. And now just evaluating this expression, we find that side length B is equal to 14.41 ft. And now we can move on to finding our final side length lowercase C. And so we just repeat this process where again, we take our a expression where we have 11.21 divided by s of 47.82 degrees. And now again, from the law of signs, we know this expression is equivalent to lowercase C divided by sine of capital C, which we found to be 59.84 degrees. And now just like we solved for lowercase B, we find that lowercase C is equivalent to 11.21 multiplied by sine of 59.84 degrees, all divided by sine of 47.82 degrees. And now just evaluating this final expression, we find that side length C is equivalent to 13.08 P. And with this, we have found our missing angle as well as both of our missing side links. And so with these values, we are left with answer choice. A where again, we found capital C is equal to 59.84 degrees. Lowercase B is equal to 14.41 ft and lowercase C is equal to 13.08 ft. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each triangle ABC.
A = 68.41°, B = 54.23°, a = 12.75 ft

Key Concepts

Law of Sines

Angle Sum Property

Trigonometric Ratios

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