Answer:
12
Step-by-step explanation:
using pythagoras theorem
here 15 is hypotenuse since it is opposite 0f 90 degree
9 and x are the other smaller sides of a triangle
according to pythagoras thorem the sum of square of two smaller sides of a triangle is equal to the square of hypotenuse. So,
9^2 + x^2 = 15^2
81 + x^2 = 225
x^2 = 225 - 81
x^2 = 144
x =
x = 12
Answer:
a = -0.3575
Step-by-step explanation:
The points A and D lie on the x-axis, this means that they are the x-intercepts of the parabola, and therefore we can find their location.
The points A and B are located where
This gives
Now given the coordinates of A, we are in position to find the coordinates of the point B. Point B must have y coordinate of y=2 (because the base of the trapezoid is at y=0), and the x coordinate of B, looking at the figure, must be x coordinate of A plus horizontal distance between A and B, i.e
Thus the coordinates of B are:
Now this point B lies on the parabola, and therefore it must satisfy the equation
Thus
Therefore
Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π → C = π - (A + B)
→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))
→ sin C = sin (A + B) cos C = - cos(A + B)
Use the following Sum to Product Identity:
sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]
cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]
Use the following Double Angle Identity:
sin 2A = 2 sin A · cos A
<u>Proof LHS → RHS</u>
LHS: (sin 2A + sin 2B) + sin 2C
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C
