Question

In triangle ABC, the measure of angle C is 90°, the measure of angle A is 57°, and side CA is 2.6 feet. Find the length of BC to the nearest tenth of a foot.

Answer 1

To find the length of BC in right triangle ABC with angle C at 90° and angle A at 57° with CA being 2.6 feet, we use the sine function. By calculating BC = 2.6 × sin(57°) and rounding to the nearest tenth, we can obtain the measure of side BC.

Step-by-step explanation:

To find the length of side BC in triangle ABC where angle C is 90°, angle A is 57°, and side CA is 2.6 feet, we can use trigonometric ratios. Given that angle A is 57 degrees, we can use the sine function which relates the opposite side to the hypotenuse in a right triangle. In this case, BC would be the opposite side of angle A.

Using the sine function:
sin(57°) = opposite/hypotenuse = BC/CA

By rearranging the equation, we can solve for BC:
BC = CA × sin(57°)

Now plug in the values:
BC = 2.6 × sin(57°)

After calculating the sine of 57 degrees and multiplying by 2.6, you would round to the nearest tenth to find the measure of side BC. Remember, since the trigonometric function gives a ratio, you need to ensure your calculator is set to the correct mode (degrees in this case) to get the correct measure for BC.