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In the right triangle △ABC shown below, the length of  𝐵𝐶― is 12 feet and sin A =  34. What is the length, in feet, of  𝐴𝐶― ?

Question

In the right triangle △ABC shown below, the length of  𝐵𝐶― is 12 feet and sin A =  34. What is the length, in feet, of  𝐴𝐶― ?

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Solution

The question seems to be missing some information. The sine of an angle (sin A in this case) is a ratio and should be a value between -1 and 1. However, in your question, sin A is given as 34 which is not possible.

Assuming that sin A is a value between -1 and 1, we can use the definition of sine in a right triangle to find the length of AC. The sine of an angle in a right triangle is defined as the length of the opposite side (BC in this case) divided by the length of the hypotenuse (AC in this case).

So, if we had a correct value for sin A, we could set up the equation sin A = BC/AC and solve for AC.

But as it stands, with sin A = 34, we cannot solve the problem as it is not a possible scenario in a right triangle. Please check the values in the question.

This problem has been solved

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