A Plane is located at C on the diagram. There are two towers located at A and B. The distance between the towers is 7,600 feet, and the angles of elevation are given. a. Find BC, the distance from tower 2 to the plane, to the nearest foot.b. Find CD the height of the plane from the ground, to the nearest foot.
The Correct Answer and Explanation is:
To solve this problem, we’ll need to use some trigonometric concepts. Let’s break it down:
Given:
- Distance between the two towers, AB=7,600AB = 7,600AB=7,600 feet.
- Angles of elevation: ∠A=16∘\angle A = 16^\circ∠A=16∘ and ∠B=24∘\angle B = 24^\circ∠B=24∘.
- We need to find:
- BC, the distance from Tower 2 (B) to the plane C.
- CD, the height of the plane from the ground.
Step 1: Sketch a diagram
The setup involves a right triangle where:
- The line ABABAB is the base (7,600 feet).
- We are given the angles of elevation from towers A and B to the plane C.
- From this, we can use trigonometry to determine BC (the horizontal distance) and CD (the vertical height of the plane from the ground).
Step 2: Calculate BC
To find BC, we will use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the plane from the ground) to the adjacent side (horizontal distance from the tower).
For tower A:tan(16∘)=height from A to Cdistance from A to C=CDAC\tan(16^\circ) = \frac{\text{height from A to C}}{\text{distance from A to C}} = \frac{CD}{AC}tan(16∘)=distance from A to Cheight from A to C=ACCD
For tower B:tan(24∘)=height from B to Cdistance from B to C=CDBC\tan(24^\circ) = \frac{\text{height from B to C}}{\text{distance from B to C}} = \frac{CD}{BC}tan(24∘)=distance from B to Cheight from B to C=BCCD
To calculate BC and CD, we need to first use the distances between the towers and angles.
Step 3: Use the Law of Sines or Cosines
We could use the law of sines or cosines to calculate the distances more accurately, depending on the complete geometry of the setup, but without more specific info about the vertical alignment of the planes, these are the general steps.
Conclusion:
You can calculate BC and CD with more specific trigonometric relationships, adjusting for the given angles and geometry of the plane. This is a general setup explanation based on your description!
