What's the value of tan K?

Question

In triangle XYZ, the measure of angle Y is 90°, YZ=12, and XZ=15. Triangle HJK is similar to triangle XYZ, where vertices X, Y, and Z, respectively, and each side of triangle HJK is 1/5 the length of the corresponding side of triangle XYZ. What's the value of tan K?

Answer 1

Triangle XYZ is a 3-4-5 right triangle

meaning its sides are in the ratio of 

3 : 4 : 5 ;  XY : 12 : 15 so XY = 9

 

HJ = (1/5)9 = 9/5

 

JK = (1/5)12 = 12/5

 

tan K = (9/5) / (12/5)

 

         = 9/12

 

         = 3/4

 

tan K = 3/4 or .75