Question

identifying trig ratio (diagram), level 1
score: 9/10 penalty: none
question
express cos c as a fraction in simplest terms.
answer attempt 1 out of 2
cos c

Explanation:

Step1: Find the hypotenuse

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Here \(a = 10\), \(b=24\). Then \(c=\sqrt{10^{2}+24^{2}}=\sqrt{100 + 576}=\sqrt{676}=26\).

Step2: Use the cosine formula

The cosine of an angle in a right - triangle is defined as \(\cos C=\frac{\text{adjacent}}{\text{hypotenuse}}\). For angle \(C\), the adjacent side to \(C\) is \(BC = 10\) and the hypotenuse \(AC=26\). So \(\cos C=\frac{10}{26}\).

Step3: Simplify the fraction

Simplify \(\frac{10}{26}\) by dividing both the numerator and the denominator by their greatest common divisor. The GCD of \(10\) and \(26\) is \(2\). So \(\frac{10\div2}{26\div2}=\frac{5}{13}\).

Answer:

\(\frac{5}{13}\)