Find the missing lengths. Give your answers in both simplest radical form and as approximations correct to two decimal places.

Question

Find the missing lengths. Give your answers in both simplest radical form and as approximations correct to two decimal places.

Given:right △XYZ with m∠X = 45° and XZ = 7Find:YZ and XY

simplest radical form YZ=

 

approximationYZ=

simplest radical form XY=

 

approximation XY=

Answer 1

then tan 45 = YZ/XZ

1 = YZ/7

YZ=7

By pytagorean, XY^2 = 7^2 + 7^2

= 49+49

= 2*49

= 98

XY^2 = 2*49 = 98

XY = 7*sqrt(2)

= 9.9

Note that since angle x=45, it is an isoceles

right triangle, in which case, the hypotenuse

is sqrt(2)* leg