Problems 103-106 are based on material learned earlier in...

Problems 103-106 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Solve triangle $A B C: a=4, b=1$, and $C=100^{\circ}$

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

Law of Cosines

A formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is particularly useful in solving triangles when two sides and the included angle (SAS configuration) are known, as it allows you to compute the third side.

Law of Sines

An equation that expresses the ratio of a side length of a triangle to the sine of its opposite angle as constant for all three sides and angles. This law is instrumental in finding unknown angles or sides once one pair of side and opposite angle is known.

SAS (Side?Angle?Side) Condition

A triangle is determined by two sides and the angle between them. This condition not only guarantees the existence of a unique triangle but also guides the use of the Law of Cosines to first find the missing side, followed by the Law of Sines to determine the remaining angles.

Triangle Angle Sum

A fundamental principle stating that the sum of the interior angles of a triangle is always 180°. This fact is used to compute the remaining angle once two of the angles have been determined.

Transcript

00:01 Okay, so for this problem, i've already set up the triangle.

00:03 We're trying to solve the triangle with a equal to 7, b equal to 10, and c equal to 100 degrees.

00:10 So based on the setup here, i have to do law of cosines.

00:13 So law of cosines will look like this.

00:15 C squared is equal to a squared plus b squared minus 2 times a, b times the cosine of c.

00:23 Whoops, times the cosine of c.

00:26 So c squared is equal to there'll be 7 squared plus 10 squared, minus 6.

00:31 2 times 7 times 10 times the cosine of 100.

00:38 I'd like to do these two separately to keep them, i don't want to combine everything together right away just because it might get a little confusing, so it'll be 149.

00:47 But this one i will do 2 times 7 times 10 times the cosine of 100.

00:56 So i'm going to be subtracting a negative 24 .3107.

01:03 So we put those together, okay, and i get 173 .311, and then i could square root here.

01:15 Okay, so i square with those and i get 13 .1, and let's go with three decimal places, 165.

01:24 Okay, so that's side c right here.

01:26 I still need to find my other angles.

01:28 I'm going to do law of signs for my next step.

01:30 So i will do, let's go with sign of a divided by the side seven...