Answer:
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
[tex]tan\theta = \frac{Perpendicular}{Base}[/tex]
As diagram is given below .
[tex]\theta = 39^{\circ}[/tex]
[tex]tan39^{\circ}= \frac{AB}{CB}[/tex]
CB = 778 feet
[tex]tan 39^{\circ} = 0.81 (Approx)[/tex]
[tex]0.81= \frac{AB}{778}[/tex]
AB = 0.81 × 778
AB = 630 .18 feet
Therefore the 630 .18 feet tall is the gateway arch .
