Answer:
9 sqrt(2) /2 = PQ
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp/ hypotenuse
sin 45 = PQ = 9
9 sin 45 = PQ
9 sqrt(2) /2 = PQ
The top is 4ft by 2 ft, area = 4 * 2=8 square feet.
The back is 1 1/2 ft by 4 feet, area = 1.5 *4 = 6 square feet.
The bottom equals the top = 8 square feet.
The front equals the back = 6 square feet.
The left side is 1 1/2 ft by 2 ft = 2 * 1.5 = 3 square feet.
The right side equals the left side = 3 square feet.
Total area = 8 + 6 + 8 + 6 + 3 + 3 = 34 square feet
The answer to the question is $4.7
X = 5/3 and m∠SPY = 8 1/3°.
Since PQ bisects the angle, the two angles formed by the bisector are equal:
11/2x - 5 = 4x - 5/2
We will first multiply everything by 2 to eliminate the fractions:
(11/2x)*2 - 5*2 = 4x*2 - (5/2)*2
11x - 10 = 8x - 5
Subtract 8x from each side:
11x - 10 - 8x = 8x - 5 - 8x
3x - 10 = -5
Add 10 to both sides:
3x - 10 + 10 = -5 + 10
3x = 5
Divide both sides by 3:
3x/3 = 5/3
x = 5/3
Now we will plug this in for x in both smaller angles and add them together to find the measure of ∠SPY:
11/2(5/3) - 5 + 4(5/3) - 5/2
55/6 - 5 + 20/3 - 5/2
We will rewrite everything using a denominator of 6:
55/6 - 30/6 + 40/6 - 15/6 = (55-30+40-15)/6 = 50/6 = 8 2/6 = 8 1/3°
