Question

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?

Answer 1

Answer: 630

Step-by-step explanation: The arch of the gateway is 18 feet tall

Answer 2

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 .