Question

question 9 (multiple choice worth 4 points)
(08 04 mc)
karren is looking at two buildings, building a and building b, at an angle of elevation of 40°. building a is 120 feet away, and building b is 60 feet away. which building is taller and by approximately how many feet?
o building a, it is around 100.69 feet taller than building b
o building a, it is around 50.34 feet taller than building b
o building b, it is around 100.69 feet taller than building a
o building b, it is around 50.34 feet taller than building a

Explanation:

Step1: Calculate height of building A

Use the tangent function: \( \tan(\theta)=\frac{h}{d}\), where \(h\) is height and \(d\) is distance. For building A, \(\theta = 40^{\circ}\), \(d = 120\) feet. So \(h_A=120\times\tan(40^{\circ})\). Using a calculator, \(\tan(40^{\circ})\approx0.8391\), then \(h_A = 120\times0.8391=100.692\) feet.

Step2: Calculate height of building B

For building B, \(d = 60\) feet. Using \(h_B = 60\times\tan(40^{\circ})\). Since \(\tan(40^{\circ})\approx0.8391\), then \(h_B=60\times0.8391 = 50.346\) feet.

Step3: Find the difference in heights

\(\Delta h=h_A - h_B\). Substitute the values: \(\Delta h=100.692-50.346 = 50.346\approx50.34\) feet. And \(h_A>h_B\)

Answer:

C. Building A, it is around 50.34 feet taller than building B