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?

Question

asked Mar 22, 2020 117k views

2 Answers

Hans Z · Answer 1 · 2020-03-28T18:38:34+0000

Answer:

630 .18 feet tall is the gateway arch .

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

$tan\theta = (Perpendicular)/(Base)$

As diagram is given below .

$\theta = 39^(\circ)$

$tan39^(\circ)= (AB)/(CB)$

CB = 778 feet

$tan 39^(\circ) = 0.81 (Approx)$

0.81= (AB)/(778)

AB = 0.81 × 778

AB = 630 .18 feet

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