In Exercises 13–16, find the area of the triangle having the give...

Question

In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit.

C = 42°, a = 4 feet, b = 6 feet

Accepted Answer

Hey, everyone. Here, we are asked to calculate the area of the triangle provided the following angle in two sides. Here we are given angles C which is 53 degrees. We then have side length A which is 11 centimeters. And lastly, we have side length B which is 17 centimeters. And we are also asked to express our results to two decimal places. Here we have four answer choice options, answer choice, A 56.27 centimeters squared. Answer B 124. centimeters squared. Answer C 74.67 centimeters squared and answer D 59.64 centimeters squared. So to calculate the area of this given triangle, we first need to notice that we have two side links and one given angle. So we need to recall the formula for an angle, given sides A and B and angle C. And recalling this formula, we have the area is equal to one half multiplied by A B multiplied by sign of angle C. So now we are given all of our information for our formula. We are given side links A and B as well. As angle C. So all we need to do is substitute in this given information into our formula. So we have the a area is equal to one half multiplied by 11 centimeters, multiplied by 17 centimeters multiplied by sine of 53 degrees. And so now we just want to plug in these values into our calculator to find our decimal approximation for our area. And so plugging this expression in, we result in the value 74. centimeters squared. And as we recall, we were asked to express our result to two decimal places. So we just need to round this value to the nearest 100th place. So rounding, we find that the area of our given triangle is approximately 74. centimeters squared. And with this value, we are left with answer choice C where again, the area of our Gibbon triangle is 74.67 centimeters squared. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit. C = 42°, a = 4 feet, b = 6 feet

Key Concepts

Law of Sines

Area of a Triangle

Trigonometric Functions

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