In A B C, given the lengths of the sides, find the measure of the given angle to the nearest ten

In A B C, given the lengths of the sides, find the measure...

Key Concepts

Triangle Geometry

Triangle geometry deals with the study of triangles, including their sides, angles, and other properties. It involves understanding how different elements such as side lengths and angle measures relate to each other and how to derive unknown parts when other parts are known.

Law of Cosines

The Law of Cosines is a crucial trigonometric formula used to relate the lengths of the sides of a triangle to the cosine of one of its angles. It is especially useful for determining unknown angles or sides when the triangle is not a right triangle.

Trigonometric Functions

Trigonometric functions, such as cosine and its inverse, are fundamental in relating the angles of a triangle to its side lengths. They enable the calculation of an unknown angle or side when combined with laws like the Law of Cosines.

Angle Measurement and Rounding

Angle measurement often involves calculating values using trigonometric functions and then converting those values into degrees or radians. Rounding is applied to achieve a desired level of precision in practical problem solving.

Transcript

00:01 So for this problem, we are being asked to find angle b, the measurement of angle b.

00:06 So i'm going to do it in red.

00:08 The information we're given is that side a is 15 .5.

00:15 So a is right across from angle a.

00:19 So this is 15 .5.

00:21 And let me label this as a.

00:24 Side b is 23 .6 so this is 23 .6 and this is the same as side b and then side c is 25 .1 and this is the same as side c.

00:49 So because we are given three sides and none of the information regarding the angles, we are going to use the law of cosines and because we are wondering.

01:01 About angle b we're going to use the formula that starts with b so it's going to be b square equals to a square plus c square minus 2 a c cosine so one way to remember this this is very similar to the particular in theorem you have three letters and whichever letter in question that you have to begin that's the letters that you're going to use for the angle.

01:35 So the next thing, my next step is substituting the information that was given to me.

01:41 So i know b is 23 .6, so this is going to be 23 .6 squared.

01:48 A is 15 .5.

01:51 So this is 15 .5 squared plus c is 25 .1 squared minus two times a again is 15 .5 squared.

02:04 Times 25 .1 or c cosine of b.

02:16 My next step is to put all this into the calculator and i have 23 .6 squared is equal to 556 .96.

02:37 Let me do the same below.

02:45 And then 15 .5 squared is 240 .20.

02:54 Plus 25 .1 squared is 630 .01 minus and i'm just going to multiply everything.

03:18 Let me get rid of this.

03:22 So 2 times 15 .5 times 25 .1 .1 is 778 .1.

03:40 Cosine of me...

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