Question

the highest looping rollercoaster is in colorado. an angle of elevation from a point 100 feet from the base of a perpendicular support beam is 49°. how tall is the support beam for the loop of the rollercoaster? round to the nearest foot. (see yellow hint below.) 132 ft 75 ft 87 ft 115 ft

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 49^{\circ}\), the adjacent side \(x = 100\) ft, and the opposite side \(y\) (height of the beam) is what we want to find. So, \(\tan(49^{\circ})=\frac{y}{100}\).

Step2: Solve for \(y\)

Multiply both sides of the equation by \(100\): \(y = 100\times\tan(49^{\circ})\). Using a calculator, \(\tan(49^{\circ})\approx1.150368\). Then \(y=100\times1.150368 = 115.0368\approx115\) ft.

Answer:

\(115\) ft