For a given right, side a = 76.4 feet and side b = 39.3, what is the measure of angle b to the nearest degree
by "right" do you mean "right triangle" ?
If so then tan B = b/a
B = tan^-1 (b/a)
To determine the measure of angle b, we need to use the trigonometric function inverses. Specifically, we will use the inverse tangent (or arctangent) function, often denoted as atan. The formula we'll use is:
angle b = atan(a/b)
Here, a represents the length of the side adjacent to angle b, and b represents the length of the side opposite angle b.
Let's substitute the given values into the formula:
angle b = atan(76.4/39.3)
Now, we can find the angle b by calculating the arctangent of the ratio a/b.
Using a scientific or graphing calculator, input the value 76.4, divide it by 39.3, and then find the inverse tangent (or arctangent) of that result.
After evaluating this expression, the resulting angle can be rounded to the nearest degree to find the measure of angle b.