Question

identifying trig ratios (diagram), level 1
score: 5/10 penalty: none
question
express cos l as a fraction in simplest terms.
answer attempt 2 out of 2
cos l

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 3\), \(b = 4\).

$$\begin{align*} c^{2}&=3^{2}+4^{2}\\ c^{2}&=9 + 16\\ c^{2}&=25\\ c&=5 \end{align*}$$

Step2: Use the cosine formula

The cosine of an angle in a right - triangle is \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). For \(\angle L\), the adjacent side is \(3\) and the hypotenuse is \(5\).
So, \(\cos L=\frac{3}{5}\)

Answer:

\(\frac{3}{5}\)