Answer:
Length of side a = 4.30 miles
Incomplete question:
The area of the regular polygon is 48 mi2. What is the length of side a? miles
Step-by-step explanation:
The number of sides of sides of the polygon is not given, so we will assume the polygon is an hexagon as shown in the attached image;
Given;
Area = 48 mi^2
Area of an hexagon using side a can be written as;
A = (3/2)√3×a^2
Making a the subject of formula
a = √(2/3√3 ×A)
Substituting the values
a = √(2/3√3 ×48)
a = √(32/√3)
a = 4.30 miles
Answer:
3.) 0.894
Step-by-step explanation:
✔️First, find BD using Pythagorean Theorem:
BD² = BC² - DC²
BC = 17.89
DC = 16
Plug in the values
BD² = 17.89² - 16²
BD² = 64.0521
BD = √64.0521
BD = 8.0 (nearest tenth)
✔️Next, find AD using the right triangle altitude theorem:
BD = √(AD*DC)
Plug in the values into the equation
8 = √(AD*16)
Square both sides
8² = AD*16
64 = AD*16
Divide both sides by 16
4 = AD
AD = 4
✔️Find AB using Pythagorean Theorem:
AB = √(BD² + AD²)
AB = √(8² + 4²)
AB = √(64 + 16)
AB = √(80)
AB = 8.9 (nearest tenth)
✔️Find sin x using trigonometric ratio formula:
Reference angle = x
Opposite side = BD = 8
Hypotenuse = AB = 8.944
Thus:
(nearest thousandth)