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In the right triangle above, if a is 3cm and tan a is 0.75, what is the length of b?

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Final answer:

In a right triangle with a given length for one leg and the tangent of one of the angles, we can use the tangent ratio to find the length of the other leg.

Step-by-step explanation:

In a right triangle, the length of the hypotenuse (c) can be found using the Pythagorean theorem, which states that a² + b² = c², where a and b are the lengths of the legs of the triangle. In this case, we are given that a = 3 cm and tan(a) = 0.75. To find the length of b, we can use the relationship between tangent and the sides of a right triangle. Since tangent is equal to the ratio of the opposite side (b) to the adjacent side (a), we can say that tan(a) = b/a. Plugging in the given values, we have 0.75 = b/3. Solving for b, we can cross-multiply to get b = 0.75 * 3 = 2.25 cm.

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