Answer
x = 3 √2
y = 1.5 √2 = (3/2) (√2)
z = 1.5 √6 = (3/2) (√6)
Step-by-step explanation
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
For this question, there are two triangles. The one with two 45° and the one with a 60°
Starting with the triangle with 45°,
Hypotenuse = 6
Opposite = x
Adjacent = x (Two of the angles being equal means two of the sides are equal).
Angle = 45°
Using trignometric ratios, we know that SOH means
Sin 45° = (Opp/Hyp)
Sin 45° = (x/6)
Cross multiply
x = 6 (Sin 45°)
Sin 45° = (√2)/2 = 0.5 √2
x = 6 (Sin 45°) = 6 (0.5 √2) = 3√2
We can then go to second triangle with 60°
Hypotenuse = x = 3√2
Opposite = z = ?
Adjacent = y = ?
Using trignometric ratios, we know that SOH means
Sin 60° = (Opp/Hyp)
Sin 60° = (z/x)
Cross multiply
z = x (Sin 60°)
x = 3√2
Sin 60° = (√3)/2 = 0.5 √3
z = x (Sin 60°)
z = 3√2 (0.5√3)
z = 1.5 √6
Then for y, we know that CAH means
Cos 60° = (Adj/Hyp)
Cos 60° = (y/x)
Cross multiply
y = x (Cos 60°)
x = 3√2
Cos 60° = 0.5
y = x (Cos 60°)
y = 3√2 (0.5)
y = 1.5 √2
Hope this Helps!!!