Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = 90° → A + B = 90° - C
→ C = 90° - (A + B)
Use the Double Angle Identity: cos 2A = 1 - 2 sin² A
→ sin² A = (1 - cos 2A)/2
Use Sum to Product Identity: cos A + cos B = 2 cos [(A + B)/2] · cos [(A - B)/2]
Use the Product to Sum Identity: cos (A - B) - cos (A + B) = 2 sin A · sin B
Use the Cofunction Identities: cos (90° - A) = sin A
sin (90° - A) = cos A
<u>Proof LHS → RHS:</u>
LHS: sin² A + sin² B + sin² C
![\text{Sum to Product:}\quad 1-\dfrac{1}{2}\bigg[2\cos \bigg(\dfrac{2A+2B}{2}\bigg)\cdot \cos \bigg(\dfrac{2A-2B}{2}\bigg)\bigg]+\sin^2 C\\\\\\.\qquad \qquad \qquad =1-\cos (A+B)\cdot \cos (A-B)+\sin^2 C](https://tex.z-dn.net/?f=%5Ctext%7BSum%20to%20Product%3A%7D%5Cquad%201-%5Cdfrac%7B1%7D%7B2%7D%5Cbigg%5B2%5Ccos%20%5Cbigg%28%5Cdfrac%7B2A%2B2B%7D%7B2%7D%5Cbigg%29%5Ccdot%20%5Ccos%20%5Cbigg%28%5Cdfrac%7B2A-2B%7D%7B2%7D%5Cbigg%29%5Cbigg%5D%2B%5Csin%5E2%20C%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cqquad%20%5Cqquad%20%3D1-%5Ccos%20%28A%2BB%29%5Ccdot%20%5Ccos%20%28A-B%29%2B%5Csin%5E2%20C)
Given: 1 - cos (90° - C) · cos (A - B) + sin² C
Cofunction: 1 - sin C · cos (A - B) + sin² C
Factor: 1 - sin C [cos (A - B) + sin C]
Given: 1 - sin C[cos (A - B) - sin (90° - (A + B))]
Cofunction: 1 - sin C[cos (A - B) - cos (A + B)]
Sum to Product: 1 - sin C [2 sin A · sin B]
= 1 - 2 sin A · sin B · sin C
LHS = RHS: 1 - 2 sin A · sin B · sin C = 1 - 2 sin A · sin B · sin C 
Answer:
2.67 seconds
Step-by-step explanation:
Distance covered by the dog = 40 ft
The rate at which the dog runs (speed) = 15 ft/s
But,
speed = 
So that,
time = 
= 
= 2
time = 2.6667 s
It would take the dog 2.67 s to mess.
Answer:
sail a = 81ft²
sail b base = 12ft
Step-by-step explanation:
question 5:
the measurements for sail A are 18ft(height) and 9ft (base)
the formula to find the the area of a triangle is (b · h) 1/2
(9 · 18) 1/2 = (162) 1/2 = 81
so ahmad will need 81ft² of fabric for sail a
question 6:
we know that the formula to find the area of a triangle is (b · h) 1/2 = a, since we know the height and the area of the triangle we plug them into the equation to find the measurement of the base.
(b · 18) 1/2 = 108
= 108/ 1/2
(b · 18) = 216
18b = 216
18b/18 = 216/18
b= 12
check your work:
(12 · 18) 1/2 = 108
(216) 1/2 = 108
108 = 108 true!
the base measurement for sail b is 12ft
hope this helps and have a great day!!
Well t would be 6/10 9/15 and u just add 3 to the numerator and 5 to the denominator
Answer:
The possible combinations of two letters is 12
Step-by-step explanation:
Here, we want to count the possible combinations of two letters
Now, for the first letter any point in time, we have 4 letters to pick from,
For the second letter we have 3 letters to pick from
So therefore, we have the possible combinations as;
4 * 3 = 12
