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Click here to see ALL problems on Trigonometry-basicsQuestion 88982: Find sinA, cosA, & tanA of the following triangle.Line AC=2 Line AB=4Angle C is a right triangle (ie. 90 degrees)Thanks! Found 2 solutions by Edwin McCravy, bucky:Answer by Edwin McCravy(19231) (Show Source): You can put this solution on YOUR website! Find sinA, cosA, & tanA of the following triangle.Line AC=2 Line AB=4Angle C is a right triangle (ie. 90 degrees) Thanks!Now we use the Pythagorean theorem to find the missing side BC:AC� + BC� = AB� 2� + BC� = 4� 4 + BC� = 16 BC� = 12 __ BC = �12 ___ BC = �4�3 _ BC = 2�3So now the triangle is: = = = = = = = = = = = = Edwin Answer by bucky(2189) (Show Source): You can put this solution on YOUR website! If you sketch triangle ABC as you described (with angle C the right angle) you can see thatside AC is one leg of the triangle & side AB is the hypotenuse. Side BC is the other legand is of unknown length..Use the Pythagorean theorem khổng lồ find the length of side BC. ..Since the problem gives you the values for AC and AB you can substitute those values andthe Pythagorean equation becomes:..Square out the known terms khổng lồ get:..Subtract 4 from both sides to lớn get:..Solve for BC by taking the square root of both sides to lớn get:..So now you know all three sides. The hypotenuse is 4, the side adjacent to lớn angle A is 2,and the side opposite lớn angle A is ..Now all you have to vị is khổng lồ use the definitions for sin A, cos A, & Tan A as follows:....As you gain a little experience you might recognize that the given triangle is a 30 - 60 - 90triangle where 30 degrees is angle B, 60 degrees is angle A, and 90 degrees is angle C..Therefore, you can kiểm tra these answers by entering 60 degrees on a scientific calculator..Then press the sin key to lớn find that sin(60) = 0.866025403.
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This will be the same answer that you will get by taking the square root of 3 & dividing it by 2..Similarly if you enter 60 degrees and press the cos key lớn find that cos(60) = 0.5This equals the above answer that cos(A) = 1/2..Finally, if you enter 60 degrees and press the chảy key to lớn find that tan(60) = 1.732050808and this is identical to the answer that tan(A) = square root of 3 that we got above..Hope this helps you to lớn see how you can work this problem..