ΔAOB is a right angled triangle. Therefore the Pythagorean Theorem applies in this situation.
θ is the angle from a standard position of the line OA
The length of the y component is √(1-0)2 +(-3-(-3))2] =√(12+ 02) = 1 A(-3,1) to B(-3,0) which is opposite
Then the length of the x-component is √[(-3-0)2 +(0-0)2] = √(9+0)= 3 B(-3,0) to O(0,0) which is adjacent
The length of vector OA is √[(-3-0)2 + (1-0)2] = √(9+1) = √(10) A(-3,1) to O(0,0) which is the hypotenuse of the triangle
θ = 180 - α
sinθ = sin(180-α) = opposite/hypotenuse = 1/√10
cosθ = adjacent/hypotenuse = -3/√10
tanθ = opposite/adjacent = 1/-3 = -1/3
α= arcsin(1/√10) ≈ 18
θ =180 -18 ≈162
Answer:
False. Correct ratio is 
Step-by-step explanation:
the ratio of sine is opposite over hypotenuse
(opposite is the side across from the angle and hypotenuse it the slant line in the triangle)
17.775 is the most precise since it has the most decimals. However, it may not be correct.
Answer:
150
Step-by-step explanation:
30 + 30 + 45 + 45 = 150
We know that x = 30 + y, because the problem says that there are 30 more football players than basketball players.
Each group has 10 more members added: x + 10 and y + 10. We can write x + 10 as 30 + y + 10 or 40 + y.
The ratio (40 + y)/(y + 10) = 3/2. You can cross multiply to get:
80 + 2y = 3y + 30
Combine like terms to get:
y = 50 members on the basketball team. Since there are 30 more members on the football team, you just add 30 to 50 to get x = 80 members on the football team.
