The length of a rectangle is 142.9 in. If the diagonal makes an angle of 32.1o with this side, find the measure of the diagonal of the rectangle rounded to the nearest tenth of an inch. let x represent the diagonal.
Draw a diagram. If the length is x, then
142.9/x = cos 32.1°
To find the measure of the diagonal of the rectangle, we can use trigonometry. Let's label the length of the rectangle as the adjacent side (a) and the diagonal as the hypotenuse (h).
From the given information, we know that the length of the rectangle is 142.9 inches, and the angle between the length and the diagonal is 32.1 degrees.
Using trigonometric functions, we can determine the length of the diagonal by using the cosine function. The cosine of an angle is equal to the length of the adjacent side divided by the length of the hypotenuse. In this case, we have:
cos(32.1°) = a / h
Rearranging the equation, we get:
h = a / cos(32.1°)
Now, substituting the value of the adjacent side (length of the rectangle) which is 142.9 inches, we can calculate the diagonal:
h = 142.9 / cos(32.1°)
Using a calculator, evaluate the cosine of 32.1 degrees, then divide 142.9 inches by the result. The resulting value will be the measure of the diagonal.
Now, rounding this value to the nearest tenth of an inch, you can report the measure of the diagonal of the rectangle.