Given: Diagram as shown a. Find ∠R to the nearest degree. b. Find QR to the nearest integer. c.

Given: Diagram as shown a. Find ∠R to the nearest degree. b....

Key Concepts

Law of Sines

The Law of Sines states that in any triangle, the ratios of the lengths of the sides to the sines of their opposite angles are equal. This principle is crucial in solving triangles, especially when dealing with non-right triangles, as it allows one to find unknown sides or angles given sufficient information.

Triangle Angle Sum Property

This property states that the sum of the interior angles of a triangle is always 180 degrees. It is used to find an unknown angle when the other two angles are known, and is a fundamental part of triangle geometry in trigonometry.

Trigonometric Ratios in Triangles

Trigonometric ratios like sine, cosine, and tangent relate the angles of a triangle to its side lengths. In the context of the Law of Sines, the sine function is used to establish relationships between angles and sides, enabling the determination of missing measurements in a triangle.

Transcript

00:01 Okay we're gonna have some little bit fun with some trig identities and some trig and some magic and you need to calculator so if we're gonna find angle we're gonna find the c you find angle r to the nearest degree we're gonna need x and so let's find x using 70 degrees and 10 so let's see because this is a right right triangle by the way, this little triangle right here, this orange one.

00:34 So let's see, 70 would be the opposite side over the hypotenuse, which is the sine, if you remember, sine of theta is equal to opposite over hypotenuse.

00:56 Okay, so i'm going to write this equation out for 70.

01:00 Sine of 70 equals x over 10.

01:06 Okay, awesome sauce.

01:09 Now to figure out x, we'll multiply both sides, multiply both sides of the equation by 10.

01:19 So we get 10 times sine of 70 equals x.

01:26 Okay, that's awesome sauce.

01:29 Now, what do we do now? so sine of 70 you can just do this on your calculator let me pause the video so i can do that on my calculator okay so sine of 70 is looks like 0 .94 so whatever this so 10 times 0 .94 times point or give me a sec sorry times 0 .94 4 that equals 9 .4 nearest degree so so let's make that a whole number we're gonna make that a whole number or we could just leave it like that 9 .4 all right so now that we have that x is 9 .4 and it doesn't really say i'm gonna do qr that there's ginger that doesn't really say anything other than that okay okay, so now i've got 9 .4.

02:29 I can say the sine of r is equal to 9 .4 over 12.

02:38 Notice that's opposite over hypotenuse.

02:42 So the sine of r is some decimal, and i don't know what that's going to be.

02:48 Let me just pause the video and check that on my calculator.

02:51 Okay, so that's 0 .078.

02:58 Okay, so now you need to, on your calculator, if we want to know what r is, we need to do on your calculator the inverse of sine.

03:08 So you do sine negative 1 of sine of r equals, i'm going to write it under here and i'll rewrite it, sine negative 1 of 0 .07 okay we'll just go out and try it again let's go over here so the sine of negative 1 of the sine of r equals the sine of you can't write today it must be friday sine negative 1 of 0 .078 okay so there's a a little button like that on your calculator i'm gonna hit mine and see what r is okay so when i get this i get that r is equal to basically 4 .5 degrees which is equal to 5 degrees well we're going to round it it's roughly equal to 5 degrees we're gonna round it because it says find r to the nearest degree okay, alright, so this is going to be 5 degrees.

04:23 Let me make sure i did that right on my calculator.

04:25 Hold on.

04:26 Okay, i need to back that up.

04:28 My brain said check it and i checked it and i was wrong...

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