The side of a triangle opposite a 58° measures 15 inches. To the nearest hundredth of an inch, what is the length of the side opposite a 53° angle
In the same triangle?
In the same triangle, the law of Sines holds
15/sin58=s/sin53
solve for s.
To find the length of the side opposite a 53° angle, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant.
Let's call the length of the side opposite the 53° angle "x". We know that the length of the side opposite the 58° angle is 15 inches and the angle opposite it is 58°.
Using the Law of Sines, we can set up the following proportion:
sin(58°)/15 = sin(53°)/x
To solve for x, we can cross-multiply and then divide:
x = (15 * sin(53°)) / sin(58°)
Now we can calculate the value of x using a calculator:
x ≈ (15 * 0.799) / 0.848
x ≈ 14.085
Therefore, the length of the side opposite the 53° angle is approximately 14.09 inches (rounded to the nearest hundredth of an inch).