Question

A park bench sits 778 feet from the base of the Gateway Arch in St. Louis, Missouri. The angle of elevation from the ground where the park bench sits to the top of the Gateway Arch is 39°. How tall is the Gateway Arch?

The Gateway is _____ feet tall.

Answer 1

Answer:630.011 feet

Step-by-step explanation:

Answer 2

The height of the Gateway Arch is 629.4 feet.

Given:

The park bench's distance from the Gateway Arch's base is (d) = 778 feet.

The angle of elevation from the ground where the park bench sits to the top of the Gateway Arch is (∅) = 39°.

To Find:

The height of the Gateway Arch (h) is =?

Solution:

The above problem is from the topic of the Application of Trigonometry.

Here, we will be using the formula to calculate the tangent of any angle;

From any angle ∅,

We can write tan(∅) =  $\frac{Opposite Side}{Adjacent Side}$

Now, in the rough figure provided in the attachment below, the angle ∅ is the angle of elevation to the top of the Gateway Arch from the park bench;

i.e., ∅ = 39°

∴ tan (∅) = $\frac{Height Of The GatewayArch}{ Distance From The Base}$

∴ tan (∅) = $\frac{h}{d}$

∴ tan (39°) = $\frac{h}{778}$

∴ h = 778 × tan (39°)

∴ h = 778 × (0.809)

∴ h = 629.4 feet.

Thus, the Gateway Arch is 629.4 feet tall.

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