A large helium balloon is tethered to the ground by two ropes. One rope is 100 ft. long and makes an 80° angle with the ground. The second rope makes a 40° angle with the ground. How long is the second rope to the nearest thousandth?

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.

(5x-1)^2= (5x)^2-2(5x)×1+(1)^2=25x^2-10x+1

yeah i know the problem you need. i am taking it right now. the answer is step 3

~mickey