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.

A  = 53°24', c = 387.1 ft

Accepted Answer

Find the missing side links in the missing angle of the right triangle express the angle in degrees and minutes where C is 90 degrees A is degrees, 36 minutes and side C is 431. centimeters. We have four possible answers. All angle B and size A and B. Let's go ahead and solve this problem. We'll first do this by drawing a triangle where we have angle C as 90 degrees or at the right angle directly across from angle C will be side C or 31. centimeters. Finally, I will label this angle on the bottom right as angle A which she knows 43 degrees, 36 minutes. Now, the first thing we can do is find angle B because we have one missing angle left, we know the sum of angles in a right triangle or just any triangle is degrees. You have 1 80 equals A plus B plus C, 1 80 with an equal angle A 43 degrees, 36 minutes plus B plus 90 degrees. Now, we can subtract 90 and 43 degrees, 36 minutes. From both sides, we will get 90 equals degrees, 36 minutes plus B and then subtracting again, we know that there are 60 seconds in a minute and 60 minutes in an hour. And here we're using minutes. So we will go ahead and subtract 60 minus 36 to find our minutes. We end up with 46 degrees 24 minutes. As a result, this will be equals to B no, we can find our side links. We have all three angles, her ankle beat 46 in angle eight, which we already have. Now, we can make use of our trick functions. We know sign over angle A will be our side. A divided by hypos C. We get a sign of 43 degrees. 36 minutes is equals to A divided by side C which is 4 31.2. We get A equals 4 31.2 sign 43 36. We can then put this into a calculator giving us a s equals to about 2 97.4 centimeters. Now can find side B by doing the same. But instead we will use cosine cosine of angle A will be our adjacent side B divided by our hypo C. We will then get side B divided by 31.2 as equals the cosine of angle A 43 we get B is equals to 4 31.2 cos 43 36 which in the calculator gives us B equals 3, 12.3 centimeters. We now have all of our measures 46 degrees 24 minutes. Side A of 2 97.4 centimeters and side B of 3, 12.3 centimeters. We then see the answer to our problem is answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Right Triangle Properties

Trigonometric Ratios

Angle Measurement Conversions

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