Solve each right triangle. In each case, C = 90°. If angle inform...

Question

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.

B  = 39°09', c = 0.6231 m

Accepted Answer

Hello, everyone. We are asked to find the missing side lengths and the missing angle of the right triangle. We want to express the angle in degrees and minutes. We are told that angle C is 90 degrees. Angle B is 42 degrees five minutes and side C is 0.6583 centimeters. Our answer choices are a side, I'm sorry. Angle A is 46 degrees. 55 minutes. Side A is 0.4886 centimeters and side B is 0.4412 centimeters B angle A is 47 degrees five minutes. Side A is 0.4412 centimeters. Side B is 0.4886 centimeters. See angle A is 47 degrees 55 minutes. Side A is 0.4886 centimeters. Side B is 0.4412 centimeters D angle A is 47 degrees 55 minutes. Side A is 0.4412 centimeters and side B is 0.4886 centimeters first. What would help me the most here is to set up a little bit of a diagram. So I'm gonna draw myself a small rate triangle just so I know where everything is. So we are told that angle C is our 90 degree angle. So that means our hypotenuse is side C which is 0.6583 centimeters. We don't know which side is A and B but it's OK. So angle A, I'm putting at the top, so side A would be across from it. Angle B, I'm putting at the bottom, right. So side B would be across from it and we are told that angle B was 42 degrees five minutes. So the first thing I'm gonna find is angle A, I know that all the angles of a triangle total 100 80 degrees. So to find angle A, I can do 180 degrees minus 90 degrees for angle C minus 42 degrees five minutes for angle B. And that'll give me the measure of angle A and when I do so we find that the measure of angle A is 47 degrees 55 minutes. So that is angle A, we know part of our answer, not all of it just yet. So now we need to find side A and side B. So let's see what we know. Um If I want to find side B, I can use angle B, so let's try side B. So side B is opposite angle B and we know the hypotenuse. So opposite over hypotenuse is S. So I'm gonna say that lower case B or the side B divided by the hypotenuse, 0.6583 equals the sign of angle B which is 42 degrees five minutes. So if I cross multiply, I get that lowercase B or side B equals 0.6583 multiplied by the s of 42 degrees five minutes. And if you're putting this in a calculator, make sure you are in degree mode, not radiant mode. And when I do this multiplication, I get 0.4412. So lowercase B, it's gonna be 0.4412 centimeters. Yeah. Well, there centimeters in there and now we need to find side A. So I'm going to do that right over here. So lowercase A. So looking at it in relation to what we have, I again, think I'm gonna use angle B side A is adjacent to it. And so I know that adjacent divided by hypotenuse is cosine. So I'm gonna say lowercase A divided by our hypotenuse of 0.6583 will equal the cosine of 42 degrees five minutes. So again, I'm gonna cross multiply to get A by itself. So A will equal 0.6583 multiplied by the cosine of 42 degrees five minutes. And again, make sure your calculator is in degree mode, not radiant mode. And when I multiply this, I get that A equals 0.4886 centimeters. So that is gonna be the length of side A. So it looks like I have all three values. So now I need to see which answer choice has all of those elements. So I want angle A to be 47 degrees 55 minutes. So that means it's answer choice C or D continuing on. I want side A to be 0.4886 centimeters and side B to be 0.4412 centimeters. So this means it's answer choice C have a nice day.

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