Question

In right triangle XYZ, the right angle is located at vertex Y. The length of line segment XY is 12.4 cm. The length of line segment YZ is 15.1 cm. Which is the approximate measure of angle YZX?

Answer 1

The measure of angle YZX is 39.4°.

Explanation:

Given information: ΔXYZ is a right angled triangle, ∠Y=90°, XY=12.4 cm, YZ=15.1 cm.

In a right angled triangle,

`\tan \theta = (opposite)/(adjacent)`

In triangle XYZ,

`\tan (\angle YZX) = (XY)/(YZ)`

`\tan (\angle YZX) = (12.4)/(15.1)`

Taking tan⁻¹ on both sides.

`\angle YZX =\tan^(-1) ((12.4)/(15.1))`

`\angle YZX =39.3925680393`

`\angle YZX \approx 39.4^(\circ)`

Therefore the measure of angle YZX is 39.4°.