(a. s."similarity in right triangles"solve for xa.) 10b.) 20c.) 14.5d.)

A. 10

Step-by-step explanation:

To find a side length of similar triangles, write two equal ratios and set them equal in a proportion. The ratios should be written using the side lengths in each triangle which correspond to each other.

This proportion compares the short side of the largest triangle to its hypotenuse and compares the short side of the smallest triangle to its hypotenuse. To solve for x, cross multiply by multiplying numerator and denominator.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

c

step-by-step explanation: