The angle of elevation from a park bench 778 feet from the base of the gateway arch in st. louis, missouri is 39 degrees. how tall is the gateway arch?

630 .18 feet tall is the gateway arch .

Step-by-step explanation:

As given

The angle of elevation from a park bench 778 feet from the base of the Gateway Arch in St. Louis, Missouri is 39 degrees.

Now by using the trignometric property

As diagram is given below .

CB = 778 feet

AB = 0.81 × 778

AB = 630 .18 feet

Therefore the 630 .18 feet tall is the gateway arch .

there are infinitely many solutions.

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.