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Triangle that has a 90 degree angle 36 degree angle and a 49 inch leg And they ask for the perimeter?
Wiki User
∙ 14y ago
It depends upon where the leg is. Assuming the 49 inch leg is opposite of the 36 degree angle, we know the third angle is 54 degrees (sum of a triangle's angles is 180 degrees). The law of sines states that the ratio of the sine of an angle to the side opposite the angle is equal for all three angles. This means that sin(36)/49 = sin(54)/x where x is the length of the side opposite the 54 degree angle. Solving that equation gets x = 67.44. Using the Pythagorean theorem, 49^2 + 67.44^2 = c^2 where c is the length of the hypotenuse. Solving yields c = 83.36. Summing the three sides together yields 49 + 67.44 + 83.36 = 199.80 inches.
If the 49 inch leg is adjacent to the 36 degree angle, swap 49 and x for the law of sines equation and solve.
Wiki User
∙ 14y ago
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