Using the Law of Cosines, use the Law of Cosines to solve the triangle. Round your answers to tw

Using the Law of Cosines, use the Law of Cosines to solve...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Solving Triangles

Solving a triangle involves using known sides and angles to determine the remaining unknown measurements of the triangle. Techniques such as the Law of Cosines and Law of Sines are pivotal in this process, with the Law of Cosines being especially useful for cases where all three sides are provided or when determining an angle with knowledge of all side lengths.

Rounding

Rounding is a process in mathematics used to reduce the number of digits in a number while maintaining its approximate value. This technique is crucial in practical applications, ensuring results are presented with a specified level of precision, such as rounding to two decimal places.

Law of Cosines

The Law of Cosines is a fundamental trigonometric theorem that extends the Pythagorean theorem to all triangles, not just right triangles. It relates the lengths of the sides of a triangle to the cosine of one of its angles, allowing for the computation of an unknown side when two sides and the included angle are known, or an unknown angle when all three sides are known.

Transcript

00:01 We're given a triangle, and we're asking us the law of cosines to solve this triangle, and to round our answer to two decimal places.

00:10 So we're given the side lengths of a triangle.

00:14 This is a side, side, side side triangle, where side a has length 75 .4, side b has length 52, and side c has length 52.

00:35 Now, to solve this triangle, we want to find the measures of angles a, b, and c.

00:39 So first i find a measure of angle a using the law of cosines.

00:47 So we have the cosine of a is equal to b squared plus c squared minus a squared over 2bc.

01:08 Plugging in this is 52 squared plus 52 squared minus 75 .4 squared over 2 times 2 .4 squared over 2 times 52 times 52.

01:25 This is approximately.

01:33 Negative 0 .051 -125.

02:11 Now, because this angle, cosine of this angle is negative, it follows that the measure of our angle a is going to be 180 degrees minus the inverse cosine about of negative.

02:28 0 .05125.

03:09 So plugging this in, this is approximately 87 .06 degrees.

03:28 Now to find the measure of angle b, we'll use law of signs, we know that the sign of b is equal to b times the sign of a over the length of a.

03:43 And this is approximately the length of side b, which is 52 times the sign of about 87 .06 degrees.

03:58 Over a, which was 75 .4...

Please give Ace some feedback