Answer:
He Melanie , use SOH CAH TOA to remember the trig functions
Step-by-step explanation:
for 14 they hyp = 22 and we know one angle of 45°, we also know that the triangle has a right angle or 90° and by inspection we can tell that the other angle is also going to be 45° so we know X and Y will be the same length, is why this is a good observation.
Use one of the trig functions with H in it b/c you know Hyp is 22, so,
SOH = Sin(Θ)= Opp / Hyp
Sin(45) = Opp / 22
Sin(45) * 22 = Opp
[tex]\sqrt{2}[/tex] / 2 * 22 = opp
11*[tex]\sqrt{2}[/tex] = opp is the exact answer, if you would like some decimal places, it's 7.7781 units, both X and Y
for 15 we can use SOH again for the bigger triangle. we know the Hyp is 24 and the angle is 30°
Sin(30) = Opp / 24
Sin(30) *24 = Opp
12 = Opp ( Because I know Sin(30) = 1/2 )
Opp is the upright between the two triangles
Use CAH Cos(Θ) = Adj / Hyp
Cos(30) = Adj / 24
Cos(30) * 24 = Adj
[tex]\sqrt{3}[/tex] /2 *24 =Adj
12[tex]\sqrt{3}[/tex] = Adj
Z = 12[tex]\sqrt{3}[/tex] or if you want some decimals 20.7846
Becasue the smaller triangle is also a 45° right triangle we know that the upright and side Y are the same lengths
then
Y = 12
You could use SOH or CAH to find the Hyp but, lets just resort to Pythagoras, and use his formula to find Hyp
Hyp = [tex]\sqrt{12^{2} +12^{2} }[/tex]
Hyp = [tex]\sqrt{288}[/tex]
hyp = 16.97
X = 16.97
:)