Question

express cos i as a fraction in simplest terms. cosi=

Explanation:

Step1: Recall cosine - ratio formula

The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$.

Step2: Identify adjacent side and hypotenuse for angle $I$

For angle $I$ in right - triangle $IJK$, the adjacent side to angle $I$ is $IJ = 30$ and the hypotenuse is $IK=34$.

Step3: Calculate $\cos I$

$\cos I=\frac{IJ}{IK}=\frac{30}{34}$.

Step4: Simplify the fraction

Reduce $\frac{30}{34}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, $\frac{30\div2}{34\div2}=\frac{15}{17}$.

Answer:

$\frac{15}{17}$