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.
To find the distance from the base of the building to the car, we can use the trigonometric function tangent. Here are the steps to solve the problem:
1. Draw a diagram: Sketch a right triangle, where the vertical side represents the height of the building (145 ft) and the angle you are given is 15°. The horizontal side of the triangle represents the distance from the base of the building to the car.
2. Identify the right triangle: In this case, the right triangle is the one formed by the height of the building, the distance to the car, and a vertical line connecting the top of the building and the car.
3. Use the tangent function: The tangent of an angle in a right triangle is the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, we want to find the length of the side adjacent to the angle, which represents the distance from the base of the building to the car.
So, the equation we will use is tan(angle) = opposite/adjacent.
In this problem, the opposite side is the height of the building (145 ft), and the angle is 15°.
4. Solve for the distance to the car: Rearrange the equation to solve for the adjacent side (distance to the car).
tan(angle) = opposite/adjacent
adjacent = opposite/tan(angle)
Plugging in the values from the problem, we have:
adjacent = 145 ft / tan(15°)
5. Calculate the tangent of the angle: Use a calculator or a trigonometric table to find the tangent of 15°.
tan(15°) ≈ 0.26795
6. Calculate the distance to the car: Substitute the values into the equation for adjacent.
adjacent = 145 ft / 0.26795 ≈ 541.04 ft
Therefore, the distance from the base of the building to the car is approximately 541.04 feet. Rounding to the nearest hundredth, the car is about 541.04 ft away.
looks like a straight-forward right-angled triangle trig question.
tan75° = x/145
x = 145tan75
= 541.15