Question

The northern lights are bright flashes of colored light between 50 and 200 miles above Earth. A flash occurs 100 miles above Earth at point C. Find the measure of ∠BDC, the portion of the Earth from which the flash is visible. Round answer to the nearest degree.

Answer 1

To find the measure of ∠BDC, we need to use the concept of similar triangles.

Step-by-step explanation:

To find the measure of ∠BDC, we need to use the concept of similar triangles. From the given information, we know that the flash occurs 100 miles above Earth at point C. Let's assume that the distance from point C to the Earth's surface at point B is x miles.

Since we have a right triangle, we can use the tangent function to calculate the angle ∠BDC. Tan(∠BDC) = Opposite/Adjacent = (100/x). Rearranging the equation, we have x = 100/tan(∠BDC).

Now, we can use the given range of 50 to 200 miles to find the possible values of ∠BDC. By substituting different values of x in the equation, we can calculate the corresponding values of ∠BDC.