Final answer:
To find the height of the flagpole, the tangent function is used with the given angle of the sun and the length of the shadow. After calculations, the height of the flagpole is found to be approximately 51 feet.
Step-by-step explanation:
To determine the height of the flagpole, we can use trigonometric functions based on the information given about the length of the shadow and the angle of the sun. Using the tangent function, which is the ratio of the opposite side to the adjacent side in a right-angled triangle, we can write the equation tan(62°) = height of flagpole / 27 feet. Solving for the height of the flagpole gives us tan(62°) * 27 feet. Using a calculator, we find that tan(62°) is approximately 1.8807, and thus the height of the flagpole is approximately 1.8807 * 27 feet, which equals to about 50.799 feet. Rounding to the nearest whole number, the height of the flagpole is approximately 51 feet. The correct answer to the question, "A flagpole casts a shadow on the ground that is 27 feet long. The angle of the sun with the ground is 62°. How tall is the flagpole?" is B) 51 feet.