In Exercises 1 to 44 , round answers according to the rounding conventions on page 448 . In Exer

In Exercises 1 to 44 , round answers according to the...

Key Concepts

Rounding Conventions

Rounding conventions refer to specific guidelines for approximating numbers to a certain degree of precision, as described in a given reference such as a textbook page. When solving problems like these, it’s important to round your final answers according to the specified rules to ensure consistency and accuracy in your calculations.

Law of Sines

The Law of Sines relates the sides of a triangle to the sines of its opposite angles. It is particularly useful in solving triangles when you are given either two angles and one side (AAS or ASA cases) or two sides and a non-included angle (SSA). This law enables you to find unknown side lengths or angles by setting up proportions between the given values and their opposite angles.

Angle Sum Property

This property states that the sum of the interior angles of a triangle is always 180°. In the context of solving triangles, knowing two angles allows you to determine the third angle by subtracting the sum of the given angles from 180°. This fundamental rule is a cornerstone in triangle geometry.

Transcript

00:01 So i have some information about a triangle, right? given any triangle, i have three angles, capital a, b, and c.

00:06 And then the sides across from the angles are the lower case versions of those angles.

00:11 Okay.

00:12 So i have angle a.

00:14 I have angle c.

00:15 If i have two angles, i can solve for a third, right? my third angle b would do all angles in a triangle at up to 180.

00:24 So i'm just going to subtract 180, minus 110, minus angle c, minus angle.

00:31 And that'll give me approximately 38 degrees exactly.

00:35 So angle b is 38 degrees.

00:39 I also know that side length b is 12.

00:42 What do i want to find next? well, since i have all my angles and only have one side length, when i have more angles than sidelines, i'm gonna use law of signs.

00:51 When i have more sides than angles, i'm gonna use law of cosine.

00:54 So i'm gonna find angle a or side length a.

00:58 For law of signs, i need the angle in the side across from each other.

01:02 So i'm going to do sign of a, 110 degrees over side length a equals.

01:08 I need another pair of angle in sidelines.

01:11 So i'm going to use b's sign of b, which is 38 degrees, all over side length of b, which is 12.

01:18 Okay.

01:19 Now that i set it up using the law of signs, i could cross multiply numerator of one fraction times the denominator of the other.

01:29 What's my goal when i set up this equation to get a by itself? so i'm going to divide by what i'm multiplying by when i move something to the other side, i do the opposite operation.

01:39 And then what i can do is just plug this all into my calculator...

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