the measure of side BC is approximately 6.52 cm.
we have a right triangle with the following information:
Hypotenuse = 8 cm
Angle A = 52.1°
Side BC = x cm (opposite to angle A)
We need to find the measure of side BC (x).
Method 1: Using Sine Function:
We know the trigonometric ratio sine (sin) is equal to the opposite side divided by the hypotenuse in a right triangle.
In this case, sin(A) = x / 8.
We are also given angle A = 52.1°.
Plugging the values, we get sin(52.1°) = x / 8.
Solving for x, we get x = 8 * sin(52.1°) ≈ 6.52 cm.
Therefore, the measure of side BC is approximately 6.52 cm.
Method 2: Using Cosine Function:
We can also use the cosine function (cos) to solve for side BC.
Cosine is equal to the adjacent side divided by the hypotenuse in a right triangle.
In this case, the adjacent side is AC, and we know AC = 8 - x (because AC = hypotenuse - BC).
Therefore, cos(A) = (8 - x) / 8.
Plugging the values, we get cos(52.1°) = (8 - x) / 8.
Solving for x, we get x = 8 - 8 * cos(52.1°) ≈ 6.52 cm.