Question

A student wants to know how far above the ground the top of a leaning flagpole is. At high​ noon, when the sun is almost directly​ overhead, the shadow cast by the pole is 99 ft long. The student holds a plumb bob with a string 33 ft long up to the flagpole and determines that the point of the plumb bob touches the ground 1111 in. from the base of the flagpole. How far above the ground is the top of the​ pole?

Answer 1

Answer:

Step-by-step explanation:

shadow/flagpole = 33 ft / xwhere x is the length of the flagpole.We know that the shadow is 99 ft long, so we can set up the equation:99 ft / x = 33 ft / 1 ftCross-multiplying, we get:99x = 33 ft²Solving for x, we get:x = 33 ft² / 99 ft x ≈ 1.11 ftThe height of the flagpole is approximately 1.11 feet.However, this measurement is not in the same units as the shadow length (which is 99 ft). To find the height of the flagpole above the ground, we need to convert the shadow length to inches:99 ft = 99 ft × 12 in/ft = 1188 inThen, we can use the Pythagorean theorem to find the height of the flagpole above the ground:h = √((1188 in)² - (111 in)²) h ≈ 1186 inSo, the top of the flagpole is approximately 1186 inches (or 98.8 feet) above the ground.