Mathematics: Triangle xyz is rotated to create the image triangle x y z . which rules could describe the rotation? check all that apply.

Triangle xyz is rotated to create the image triangle

lashaaungas

25.05.2022

45.7

Step-by-step explanation:

Hello there!

We can calculate the missing angle using trigonometry

here are the trigonometric ratios

sin = opposite over hypotenuse

cos = adjacent over hypotenuse

tan = opposite over adjacent

We are given x's opposite side length (8) and x's adjacent side length (7.8)

we are given the information to use the trigonometric ratio tangent

so now we create an equation (remember tan - opposite over tangent)

$tan(x)=\frac{8}{7.8}$

now we solve for x

$\frac{8}{7} =1.025641026$

we're left with

tan(x) =1.025641026

finally we want to get rid of the tan

To do so we take the inverse of tan (arctan^-1) and apply it to each side

$arctan^-^1tan(x)=x\\arctan^-^1(1.025641026)=45.7252243$

so x = 45.7252243

finally we round to the nearest tenth and get that the answer is

45.7

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