Question

Isabel and Helena have built a frame and covered it with cloth. The frame is in the shape of a right triangle , AABC , with side lengths 6 ft ft, and 10 ft. They use a vertical pole AE to raise corner A 3 ft as shown What is the distance ED from the base of the pole to the edge of the frame? Round to the nearest foot

Answer 1

Explanation:

all triangles here are right-angled.

ABC, ADB, ADC, AED.

let's say CD = x, AD = height

just by using Pythagoras :

8² = height² + (10-x)² = height² + 100 -20x + x²

64 = height² + 100 -20x + x²

6² = height² + x²

36 = height² + x²

64-36 = 100 - 20x

28 = 100 - 20x

-72 = -20x

x = 72/20 = 3.6 ft

6² = height² + 3.6²

36 = height² + 12.96

height² = 23.04

height = 4.8 ft

height² = ED² + 3²

23.04 = ED² + 9

ED² = 14.04

ED = 3.746998799... ft ≈ 4 ft