Question

Let ABC be a right triangle with right angle at C. Let D and E be points on AB with D between A and E such that CD and CE trisect C. Ifthen tan B can be written as m/n, where m and n are relatively prime positive integers, and p is a positive integer not divisible by the square of any prime. Find m +n + p.​

a) 23
b) 30
c) 32
d) 38

Answer 1

The question seeks to calculate tan B in a right-triangle without sufficient information provided; thus, it cannot be answered as posed.

Step-by-step explanation:

The question involves solving for tan B in a right triangle ABC with angle C being the right angle, with points D and E on AB such that CD and CE trisect angle C. Utilizing the Pythagorean theorem and trigonometric identities, we could find the lengths of the sides of the triangle and subsequently calculate tan B. However, the problem as posed lacks specific measurements or ratios, making it unsolvable without additional information. It's important to note that any such calculation would involve determining the length of the opposite and adjacent sides relative to angle B and using the definition of the tangent function (tan B = opposite/adjacent).