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Find the measure of each side indicated.

Find the measure of each side indicated.-example-1
User Mushfiq
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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.

User DennisW
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