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

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 = 32 ft, c = 51 ft

Accepted Answer

Find the missing side length and missing angles of the right triangle express the angles in degrees. But we have C equals 90 B equals 18 centimeters and side C equals 35 centimeters. We have four possible answers with missing angles A and B and missing side A. Let's first make a triangle to see what we have part of the draw triangle. We see we have angle C which is the right angle. Side B and side C side, CS are at hot nudes at 35 centimeters. Side B we will say is this side of the left of 18 centimeters. Now, we need to find angles A and B side A. Now we can first find our missing side A. We know the Pythagorean theorem is A squared plus B squared equals C squared. Now we're missing side A but we have B and C, we get A squared plus 18 squared equals squared. Now A squared will be 35 squared minus 18 squared, which means side A will be the square root of 35 squared minus squared. If we were to simplify, we get side A is equals to 30 centimeters. Now, we can find one of our angles, let's say we find our angle B. Now we noticed angle B can be modeled with a sign function where we have our opposite side B divided by a high upon news C, we get sine BS equals to pay divided by 35. Now define B, we will take the arc sign of both sets with the arc sign of 18 divided by 35 which in the calculator simplifies to 30.9 degrees. Finally and go A can we model by knowing that we have 100 80 degrees in a triangle, we have one missing angle, which means we have 1 80 equals A plus B plus C, which means we have a plus 30.9 plus 90. If we were to solve for A, we will subtract 30.9 and 90 giving us 59.1 degrees. We now have all of our values 30 centimeters for sign A 30.9 degrees for angle B and 59.1 degrees for angle A. If we look at our possible answers, we see our answer. This answer. A OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

Key Concepts

Right Triangle Properties

Pythagorean Theorem

Trigonometric Ratios and Angle Conversion

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