2020 · Q56
On a plane area there are two vertical towers separated by 100 feet apart. The shorter tower is 40 feet tall. A pole of length 6 feet stands on the line joining the base of two towers so that the tip of the towers and tip of the pole are also on the same line. If the distance of the pole from the shorter tower is 75 feet, then what is the height of the taller tower (approximately)?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A85 feet
- B110 feet
- C125 feet
- D140 feet
Explanation
Put the pole's base at 0, the shorter tower's base at 75 and the taller tower's base at 175 (the pole stands on the far side of the shorter tower). By similar triangles, the height H of the taller tower satisfies (H − 6)/175 = (40 − 6)/75, giving H = 6 + 34 × 7/3 ≈ 85 ft. The exact value 85.33 ft rounds to the listed option 85 ft.