Question

in $\triangle ijk$, the measure of $angle k = 90^{circ}$, $ik = 20$, $ji = 29$, and $kj = 21$. what is the value of the cosine of $angle i$ to the nearest hundredth?

Explanation:

Step1: Recall the cosine formula in a right - triangle

In a right - triangle \(\triangle IJK\) with \(\angle K = 90^{\circ}\), the cosine of an acute angle \(\angle I\) is given by \(\cos\angle I=\frac{\text{adjacent side}}{\text{hypotenuse}}\).

Step2: Identify the adjacent side and hypotenuse for \(\angle I\)

The adjacent side to \(\angle I\) is \(IK\), and the hypotenuse is \(JI\).
We know that \(IK = 20\) and \(JI=29\).

Step3: Calculate \(\cos\angle I\)

Using the formula \(\cos\angle I=\frac{IK}{JI}\), substitute \(IK = 20\) and \(JI = 29\) into the formula.
\(\cos\angle I=\frac{20}{29}\approx0.69\)

Answer:

\(0.69\)