Question

express tan o as a fraction in simplest terms.
answer attempt 1 out of 2
tan o =
(right triangle with right angle at p, pq = 14, oq = 50)

Explanation:

Step1: Find the length of OP

In right triangle \( OPQ \), by the Pythagorean theorem \( OQ^2 = OP^2 + PQ^2 \). We know \( OQ = 50 \) and \( PQ = 14 \), so \( OP = \sqrt{OQ^2 - PQ^2} = \sqrt{50^2 - 14^2} = \sqrt{2500 - 196} = \sqrt{2304} = 48 \).

Step2: Calculate \( \tan O \)

The tangent of an angle in a right triangle is \( \tan \theta = \frac{\text{opposite}}{\text{adjacent}} \). For \( \angle O \), the opposite side is \( PQ = 14 \) and the adjacent side is \( OP = 48 \). So \( \tan O = \frac{PQ}{OP} = \frac{14}{48} \), simplify this fraction by dividing numerator and denominator by 2, we get \( \frac{7}{24} \).

Answer:

\(\frac{7}{24}\)