Can some please explain what I have to do to get the answer?

An airplane passes directly over Seneca
High School. A student at Cherokee High
School, which is 4.3 miles away, finds the
angle of elevation of the plane to be 19°.
Find the altitude of the plane.

make a sketch to see that

tan 19° = height/4.3
height = 4.3tan19°
= ..

tan 19° = height/4.3 miles

h= 4.3 x tan 19°
h = 1.48 miles

To find the altitude of the plane, we can use trigonometry.

Step 1: Draw a diagram representing the situation. Label the location of Seneca High School as point S, the location of Cherokee High School as point C, and the position of the airplane as point A. Draw a straight line connecting points S and C. Label the angle of elevation as 19°.

Step 2: From the information given, we know that SC (the distance between Seneca and Cherokee) is 4.3 miles.

Step 3: Let's denote the altitude of the plane as h.

Step 4: In the right triangle formed by points S, A, and C, the side opposite the angle of elevation is the altitude (h), the side adjacent to the angle is the distance between the schools (4.3 miles), and the hypotenuse is the line connecting the schools.

Using the trigonometric relationship of tangent, we can write the equation:

tan(19°) = h / 4.3

Step 5: Rearrange the equation to solve for h. Multiply both sides of the equation by 4.3:

h = 4.3 * tan(19°)

Step 6: Calculate the value of h using a calculator:

h ≈ 1.61 miles

Therefore, the altitude of the airplane is approximately 1.61 miles.

To find the altitude of the plane, we can use trigonometry and the information given in the problem. Let's break down the steps on how to solve this problem:

1. Draw a diagram: Draw a triangle to represent the situation. Label the corners as follows: Seneca High School (S), Cherokee High School (C), and the airplane (A). Draw a line segment from S to A and another line segment from C to A.

2. Identify the given information: The problem states that the distance between Cherokee High School (C) and the airplane (A) is 4.3 miles. It also mentions the angle of elevation from C to A is 19°.

3. Identify what you need to find: We need to find the altitude of the plane.

4. Apply the trigonometric ratio: In this case, we can use the tangent ratio since we have the angle of elevation and the opposite and adjacent sides of the triangle. Recall that tangent is defined as the ratio of the opposite side to the adjacent side.

In this triangle, the opposite side is the altitude of the plane, and the adjacent side is the distance from Cherokee High School to the plane (4.3 miles). Therefore, we can set up the equation as:

tan(19°) = altitude / 4.3

5. Solve for the altitude: Rearrange the equation to solve for the altitude:

altitude = tan(19°) * 4.3

Using a calculator, evaluate the tangent of 19° and multiply it by 4.3 to find the altitude. The result will be the answer you're looking for.

By following these steps, you should be able to find the altitude of the plane passing over Seneca High School.