Final answer:
To determine the length of OP, we use the cosine of angle O (37 degrees), adjacent side ON (72 feet), and the fact that angle P is 90 degrees to set up the equation OP = ON / cos(37 degrees), which can be calculated for the exact length.
Step-by-step explanation:
To find the length of OP when we know the length of ON and the measures of angles O and P in a right triangle, since angle P is given as 90 degrees, we can use trigonometric functions. Let's assume angle O is at the origin, ON represents the adjacent side to angle O, and OP is the hypotenuse in this scenario. Since we have a right-angled triangle, we can use the cosine function, which is defined as the adjacent side divided by the hypotenuse (cosine = adjacent/hypotenuse).
First, we calculate the cosine of angle O:
cos(37°) = ON/OP
OP can then be found by rearranging the formula:
OP = ON / cos(37°)
Given that ON is 72 feet, and using a calculator to find cos(37°), we have:
OP = 72 / cos(37°)
Now, calculate the actual value to find the length of OP in feet.