A man stands on his balcony, 120 ft above the ground. He looks at the ground, with his sight line forming an angle of 50 degrees with the building, and sees a bus stop. The function d = 120 sec θ models the distance form the man to any object given his angle of sight θ. How far is the bus stop from the man? Round your answer to the nearest foot.

A. 187 ft.
B. 92 ft.
C. 77 ft.
D. 157 ft.

(120)cos(50°)

77 ft
hope this helps : )

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Well, the man seems to have a bus-tiful view from his balcony!

To find the distance to the bus stop, we can use the equation given: d = 120 sec θ. Given that he is looking at the ground with an angle of 50 degrees, let's plug that into the equation:

d = 120 sec 50

Now, let's calculate:

d ≈ 120 * (1.901)

After doing the math, the distance to the bus stop is approximately 228.12 ft.

Since we need to round our answer to the nearest foot, the correct option would be:

A. 187 ft.

Hope that brought a little cheer to your day!

To find the distance from the man to the bus stop, we can use the given function: d = 120 sec θ.

In this case, the angle of sight θ is 50 degrees. Let's substitute this value into the function:

d = 120 sec 50

Using a calculator, we can evaluate the secant function of 50 degrees, which is approximately 1.281. So, the equation becomes:

d ≈ 120 * 1.281

Thus, d ≈ 153.72 ft.

Rounding this distance to the nearest foot, we get approximately 154 ft.

Therefore, the correct answer is not listed among the options provided.

sec(θ) = 1/cos(θ)

so the given formula gives:
distance = 120/cos(θ).
You can use your calculator to find the distance and make your choice accordingly.