A cellular telephone tower that is 150 feet tall is placed on top of a mountain that is 1200 feet above sea level. What is the angle of depression from the top of the tower to a cell phone user who is 5 horizontal miles away and 400 feet above sea level

87.9391 degrees

Step-by-step explanation:

The top of the cellular phone tower will be at 1200 + 150 = 1350 feeet above sea level.

The cell phone user is at 400 feet above sea level, so the difference of height between the cellular phone tower and the cell phone user is 1350 - 400 = 950 feet.

The horizontal distance between then is 5 miles, which is 5 * 5280 = 26400 feet.

To calculate the angle, we need to imagine a triangle, where the angle is at the top of the tower, the adjacent cathetus is 950 feet, and the opposite cathetus is 26400 feet.

The relation between opposite cathetus and adjacent cathetus is the tangent, so:

tan(angle) = 26400 / 950 = 27.7895

angle = 87.9391 degrees

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12