Question

Line segment YV of rectangle YVWX measures 24 units.

Rectangle Y V W X is shown. A diagonal is drawn from point X to point V. The lengths of sides Y V and X W are 24 units. The angle of V X W is 30 degrees, the angle of X W V is 90 degrees, and the angle of X V W is 60 degrees.

What is the length of line segment YX?

8 units
8 StartRoot 3 EndRoot units
12 units
12 StartRoot 3 EndRoot units

Answer 1

clickable version: https://us-static.z-dn.net/files/d24/58d25397fc425435b359b300213fd28e.jpg

Answer 2

notice how XYW is a 30-60-90 triangle. therefore, the side length ratios are: x, x*sqrt(3), 2x, where x = the length of the side across from the 30 degree angle, x*sqrt(3) is the other leg, and 2x is the hypotenuse

it wants the length of YX

because YVWX is a rectangle, opposite sides are congruent. therefore, YX is congruent to VW. also, YV is congruent to XW.

VW is the side across from the 30 degree angle (so our "x" side).

XW is the side across from the 60 degree angle (so our x*sqrt(3)) side. as stated earlier, YV is congruent to XW, which is equal to 24, so XW = YV = 24 = x*sqrt(3)

solve for x. since YX is equal to x, the x-value is your solution.

I know this is a lot, so please let me know if any of the individual steps are confusing you, or you just want to check your solution.