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
6( x - 4) = 7
6 x - 24 = 7
6 x = 7 + 24
6 x = 31
x = 31/6
6 ( 31/6 - 4) = 7
186/6 - 24 = 7
186/6 = 144/6 = 7
42/6 = 7
7 = 7
Answer:
x = 20√2 and y = 20√3.
or x = 28.28 and y = 34.64 to the nearest hundredths.
Step-by-step explanation:
Take the 2 'inside' triangles. They are similar.
So we have x / (60-40) = 40 / x
x/ 20 = 40 /x
x^2 = 800
x = √800
x = 20√2
y = √(800 + 20^2)
= √(1200)
= 20√3.
Answer:
11
Step-by-step explanation:
3+(−3)^2−(9+7)^0
=3+9−(9+7)^0
=12−(9+7)^0
=12−16^0
=12−1
=11
any number to the power of 0 is ALWAYS 1
(32 ft) x (30 ft + 5/12 ft) = (960 ft² + 13-1/3 ft²) = 973-1/3 feet²
