Question

identifying trig ratios (diagram), level 1
score: 6/10 penalty: none
question
express tan o as a fraction in simplest terms.
answer attempt 1 out of 2
tan o = submit answer

Explanation:

Step1: Find the length of the adjacent side

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Let the adjacent side to angle \(O\) be \(x\), the opposite side to angle \(O\) is \(14\), and the hypotenuse \(c = 50\). Then \(x=\sqrt{50^{2}-14^{2}}=\sqrt{(50 + 14)(50 - 14)}=\sqrt{64\times36}=48\).

Step2: Calculate \(\tan O\)

The formula for \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For angle \(O\), the opposite side is \(14\) and the adjacent side is \(48\). So \(\tan O=\frac{14}{48}=\frac{7}{24}\).

Answer:

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