Question

In ΔIJK, the measure of ∠K=90°, KI = 5.3 feet, and JK = 2.1 feet. Find the measure of ∠I to the nearest tenth of a degree. I

Answer 1

`\angle I = 21.6 ^\circ` is the correct answer.

Explanation:

Please refer to the attached figure.

`\triangle IJK` is shown with the following measurements:

`\angle K = 90^\circ`

Side KI = 5.3 ft

Side JK = 2.1 ft

To find :
`\angle I` = ?

Using trigonometric identity for tangent of an angle:

`tan\theta = \frac{\text{Perpendicular}}{\text{Base}}`

Here
`\theta = \angle I`

Perpendicular is side JK.

Base is side KI.

Putting the values in above formula:

`tan\theta = \frac{\text{JK}}{\text{KI}}\\\Rightarrow tan\theta = (2.1)/(5.3)\\\Rightarrow tan\theta = 0.3962\\\Rightarrow \theta = 21.6^\circ`

Hence,
`\angle I = 21.6 ^\circ` is the correct answer.