Question

express tan o as a fraction in simplest terms.

(image of a right triangle opq with right angle at p, pq = 14, oq = 50)

answer attempt 1 out of 2
tan o = blank submit answer

Explanation:

Step1: Find the length of side \(OP\)

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) in right - triangle \(OPQ\), where \(c = OQ=50\), \(b = PQ = 14\), and \(a=OP\).

$$OP=\sqrt{OQ^{2}-PQ^{2}}=\sqrt{50^{2}-14^{2}}=\sqrt{(50 + 14)(50 - 14)}=\sqrt{64\times36}=48$$

Step2: Calculate \(\tan O\)

The definition of \(\tan\) in a right - triangle is \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For angle \(O\), the opposite side to \(O\) is \(PQ = 14\) and the adjacent side to \(O\) is \(OP = 48\).
\(\tan O=\frac{PQ}{OP}=\frac{14}{48}=\frac{7}{24}\)

Answer:

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