Answer:
Explanation:
Hello! Since this is a right triangle, the three things we would be able use to solve for x and y are tangent, cosine, and sine.
The first thing we could do is solve for x (it doesn't matter what you do first, though). The side measuring 6 is opposite from the 90 degree angle, meaning it is the hypotenuse. The side measuring x is opposite from the 60 degree angle, meaning it is the opposite side from the 60 degree angle. The side measuring y forms the 60 degree angle and is not the hypotenuse, meaning it is the adjacent side to the angle measuring 60 degrees. Now that we know this, here are some formulas:
Sine = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent
Since we know that x is the opposite side and 6 (our known value) is the hypotenuse, what is the only formula using the opposite side and hypotenuse? Sine!
Sine = Opposite/Hypotenuse
Sine (60) = x/6
Sine (60) x 6 = x
Here is something to help you remember this: SOH--CAH--TOA
Sine-Opp-Adj--Cosine-Adj-Hyp--Tangent-Opp-Adj.
Solve for sine 60 degrees on your calculator by pressing the button saying sin and then typing the number (60).
((the square root of three)/2) x 6 = x
3 x the square root of three = x.
So, x = 3(the square root of three).
C and d both have options saying that x = 3(square root of three), so we will have to solve for y to find the right answer.
y is the adjacent side to 60 degrees, and now we can either use x or 6 to solve for this problem. I will use 6, the hypotenuse. We will need to use adjacent/hypotenuse = cosine (__)
cosine (__) = adjacent/hypotenuse
cosine (60) = y/6
cosine (60) x 6 = y
Solve for cosine 60 on your calculator by pressing sin and then 60.
1/2 x 6 = y
3 = y.
y = 3 and x = 3(the square root of three)
So the answer is d.