Question

find the cosine of ∠i. simplify your answer and write it as a proper fraction, improper fraction, or whole number. cos(i) =

Explanation:

Step1: Find side IJ via Pythagoras

$$IJ = \sqrt{IK^2 - JK^2} = \sqrt{74^2 - 70^2} = \sqrt{5476 - 4900} = \sqrt{576} = 24$$

Step2: Define cosine of ∠I

$\cos(I) = \frac{\text{adjacent to } \angle I}{\text{hypotenuse}}$

Step3: Substitute values and simplify

$\cos(I) = \frac{IJ}{IK} = \frac{24}{74} = \frac{12 \times 2}{37 \times 2} = \frac{24}{74} = \frac{12}{37}$

Answer:

$\frac{24}{37}$