Wendy spots a pizza delivery car as she is looking down at a 15° angle from the top of her apartment building, which is 145 ft tall. How far away is the car from the base of the building? Round to the nearest hundredth.
A. 45.98 ft
B. 3.56 ft
C. 38.85 ft
D. 68.78 ft
I keep following the tan^-1(h/d) formula for this but it won't give me any of the multiple choice answers. I've even done it through a calculator (15 = tan^-1[145/x]). I also did 15/tan(145) and 15/tan^-1(145).
Tan 15 = h/d
Tan 15 = 145/d
d = 145/Tan 15 = 541.2 Ft.
Or if the angle between the line of
sight and the ver.(145Ft) is 15o, then
Tan 15 = d/145
d = 145*Tan 15 = 38.85 Ft.
To solve this problem, you need to use trigonometry, specifically the tangent function. Let's break it down step by step:
1. Draw a diagram: Draw a right triangle representing the situation described in the problem. Label the vertical side of the triangle as the height of the building (145 ft) and the angle between the observer's line of sight and the horizontal ground as 15°.
2. Identify the trigonometric relationship: In this case, we want to find the distance from the base of the building to the car, which is the horizontal side of the triangle. The tangent function relates the angle and sides of a right triangle as follows: tan(angle) = opposite / adjacent.
3. Identify the known values: We know the height of the building (145 ft) and the angle (15°). We are trying to find the length of the adjacent side (distance from the base of the building to the car).
4. Set up the equation: Using the tangent function, we can set up the equation as follows: tan(15°) = 145 ft / x, where x is the distance from the base of the building to the car.
5. Solve for x: To find x, we need to isolate it in the equation. Start by rearranging the equation to solve for x: x = 145 ft / tan(15°).
6. Calculate the value of x: Using a calculator, evaluate the expression to find the value of x. Make sure your calculator is set to use degrees mode. The result is approximately 525.49 ft.
7. Round to the nearest hundredth: The question asks you to round the answer to the nearest hundredth. The nearest hundredth of 525.49 ft is 525.50 ft.
So, the correct answer is not among the options you provided. The correct answer would be approximately 525.50 ft.