Given that the angle opposite side BC is 30 degrees, we can use trigonometric ratios to find the values of a and b.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Therefore, we have:
sin(30 degrees) = opposite/hypotenuse
sin(30 degrees) = a/10
a = 10 * sin(30 degrees)
a = 10 * 0.5
a = 5
Similarly, the cosine of an angle is defined as the ratio of the length of the side adjacent the angle to the length of the hypotenuse. Therefore, we have:
cos(30 degrees) = adjacent/hypotenuse
cos(30 degrees) = b/10
b = 10 * cos(30 degrees)
b = 10 * sqrt(3)/2
b = 5 * sqrt(3)
What are the exact values of a and b?
Right triangle A B C is shown with labeled sides and one labeled angle. Side A B is the hypotenuse and it is labeled 10. Side B C is the height and it is labeled a. Side C A is the base and it is labeled b. The angle opposite side B C is 30 degrees.
1 answer
1 answer