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.
Tower 1:
Base angle = 16°
Tower 2:
Base angle = 24°
To solve this problem, we will use trigonometry functions.
a. Let's start by finding AB, the distance between the towers. We can use the tangent function and the given angle of elevation for tower 1:
tan(16°) = AB/BC
AB = BC * tan(16°)
Similarly, we can use the tangent function and the given angle of elevation for tower 2 to find AB:
tan(24°) = AB/BC
AB = BC * tan(24°)
Since both expressions for AB are equal, we can set them equal to each other and solve for BC:
BC * tan(16°) = BC * tan(24°)
BC = AB / (tan(16°) + tan(24°))
BC ≈ 13,928 feet (to the nearest foot)
b. Now that we know BC, we can use the tangent function and the given angle of elevation for tower 2 to find CD:
tan(24°) = CD/BC
CD = BC * tan(24°)
CD ≈ 6,046 feet (to the nearest foot)