Question

express tan o as a fraction in simplest terms.
answer
attempt 1 out of 3
tan o =

Explanation:

Step1: Find the length of OP

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here \(c = 50\), \(b=14\), and \(a = OP\).

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

Step2: Calculate \(\tan O\)

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

$$\tan O=\frac{PQ}{OP}=\frac{14}{48}$$

Simplify the fraction \(\frac{14\div2}{48\div2}=\frac{7}{24}\)

Answer:

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