Question

If a building casts a shadow 150 feet from its base, and a yardstick casts a shadow of 2 feet, how tall is the building? use trigonometric functions to solve the problem

Answer 1

We can use the tangent function to solve this problem. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the angle is the angle of elevation from the tip of the building to the top of the building.

Let h be the height of the building. Then, we have:

tan(theta) = h / 150

where theta is the angle of elevation.

Similarly, we can use the same formula to find the length of the shadow of the building:

tan(theta) = h / x

where x is the length of the shadow of the building.

We know that the length of the shadow of the yardstick is 2 feet. Therefore, we have:

tan(theta) = 1 / 2

Now we can set the two expressions for tan(theta) equal to each other:

h / 150 = 1 / 2

Solving for h, we get:

h = 150 * (1 / 2) = 75 feet

Therefore, the height of the building is 75 feet.

Step-by-step explanation:

Answer 2

Answer: 225

Explanation: tan θ = 3/2 = 1.5 Height = tan θ × adjacent = 1.5 × 150' = 225'

The correct answer is: 225'