Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π and cos A = cos B · cos C
scratchwork:
A + B + C = π
A = π - (B + C)
cos A = cos [π - (B + C)] Apply cos
= - cos (B + C) Simplify
= -(cos B · cos C - sin B · sin C) Sum Identity
= sin B · sin C - cos B · cos C Simplify
cos B · cos C = sin B · sin C - cos B · cos C Substitution
2cos B · cos C = sin B · sin C Addition
Division
2 = tan B · tan C
<u>Proof LHS → RHS</u>
Given: A + B + C = π
Subtraction: A = π - (B + C)
Apply tan: tan A = tan(π - (B + C))
Simplify: = - tan (B + C)
Substitution: = -(tan B + tan C)/(1 - 2)
Simplify: = -(tan B + tan C)/-1
= tan B + tan C
LHS = RHS: tan B + tan C = tan B + tan C 
Answer:
x = 67°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°
Subtract the sum of the 2 angles from 180 for x , that is
x = 180° - (38 + 75)° = 180° - 113° = 67°
Answer:
Step-by-step explanation:
The circular city park has a sidewalk directly through the middle that is 111 - feet long. This means that the diameter of the park is 111 feet.
The formula for determining the the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circular floor.
π is a constant whose value is 3.14
From the information given,
Diameter = 111 feet
Radius = diameter/2 = 111/2 = 55.5 feet.
Area of park = 3.14 × 55.5² = 9671.985 feet²
If each bag of fertilizer covers 50 square feet, then the number of bags needed is
9671.985/50 = 193.44 bags
