The Student Council is making six right triangular pennants to promote school spirit. Each right triangle is 9 inches high and 2
2 answers:
Answer:
Total area of six pennant is 16 feet²
Step-by-step explanation:
The student is making six right triangular pennants to promote school spirit.
Each right triangle is 9 inches high and 2 feet long.
we will convert the height of the triangle from inches to feet.
12 inches = 1 feet
9 inches = feet
Now we know each triangle is 1.33 feet high and 2 feet long.
Area of the triangular pennant = 1.33×2 = 2.67 feet²
Area of 6 pennant = 2.67×6 = 16 feet²
Therefore, area of six pennant will be 16 feet².
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Givens
y = 2
x = 1
z(the hypotenuse) = √(2^2 + 1^2) = √5
Cos(u) = x value / hypotenuse = 1/√5
Sin(u) = y value / hypotenuse = 2/√5
Solve for sin2u
Sin(2u) = 2*sin(u)*cos(u)
Sin(2u) = 2() = 4/5
Solve for cos(2u)
cos(2u) = - sqrt(1 - sin^2(2u))
Cos(2u) = - sqrt(1 - (4/5)^2 )
Cos(2u) = -sqrt(1 - 16/25)
cos(2u) = -sqrt(9/25)
cos(2u) = -3/5
Solve for Tan(2u)
tan(2u) = sin(2u) / cos(2u) = 4/5// - 3/5 = - 0.8/0.6 = - 1.3333 = - 4/3
Notes
One: Notice that you would normally rationalize the denominator, but you don't have to in this case. The formulas are such that they perform the rationalizations themselves.
Two: Notice the sign on the cos(2u). The sin is plus even though the angle (2u) is in the second quadrant. The cos is different. It is about 126 degrees which would make it a negative root (9/25)
Three: If you are uncomfortable with the tan, you could do fractions.