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?
A .34.8°
B .39.4°
C .50.6°
D. 55.2°

Answer 1

we know that

In the right triangle XYZ

$tan (YZX)=\frac{opposite\ side\ angle\ YZX}{adjacent\ side\ angle\ YZX}$

in this problem

$opposite\ side\ angle\ YZX=XY=12.4\ cm\\adjacent\ side\ angle\ YZX=YZ=15.1\ cm$

substitute the values

$tan (YZX)=\frac{12.4}{15.1}$

$Angle (YZX)=arc\ tan (12.4/15.1)$

$Angle (YZX)=39.4\°$

therefore

the answer is the option

B .39.4°

Answer 2

Angle YZX=Z
Data:
opposite=12.4
adjacent=15.1

tan Ф= opposite/adjacent
tan Z=12.4/15.1
tan Z=0.82
Z=tan⁻¹(0.82)≈39.4

Answer: B.  39.4º