Final answer:
The approximate value for angle B in a right triangle, when the ratio of the opposite leg to the hypotenuse is 0.67, can be calculated using the arcsine function. It is approximately 42.09 degrees.
Step-by-step explanation:
To approximate the angle bee (we'll refer to it as angle B), given the ratio of the opposite leg to the hypotenuse is 0.67, we need to use the inverse trigonometric function for sine since the given ratio corresponds to sine in a right triangle. Specifically, the function we will use is arcsine (or sin-1).
The formula relating an angle and the opposite side over hypotenuse in a right triangle is sin(angle) = opposite/hypotenuse. To find the angle when we know the ratio, we reverse this using the inverse sine function: angle = sin-1(opposite/hypotenuse). This gives us:
angle B = sin-1 (0.67).
Using a calculator, we find that:
angle B is approximately 42.09 degrees.
Remember that we're asked for an acute angle in a right triangle which assures that our angle measurement makes sense, as acute angles are between 0 and 90 degrees.