Respuesta :
[tex]360 \div 6 = 60 \\ 60 \div 2 = 30 \\ \frac{1}{2} (2.5 \sqrt{3} )(5) \\ 6(6.25 \sqrt{3} ) = 65.0[/tex]
Answer for #2 is A
3. D
Answer: The correct options are (2). A, (3). A.
Step-by-step explanation: The calculations are as follows:
(1) We are to given the area of a regular hexagon with radius 5 in.
The AREA of a regular hexagon with side 'a' units is given by
[tex]A=\dfrac{3\sqrt3}{2}a^2.[/tex]
We know that the radius of a regular hexagon is equal to the length of each side, so we have
a = 5 in.
Therefore, the area of the hexagon will be
[tex]A=\dfrac{3\sqrt3}{2}\times 5^2=1.5\times 1.732\times 25=64.95\sim 65~\textup{in}^2.[/tex]
Thus, (A) is the correct option.
(2) Given that two adjacent sides of the triangle measure 1.32 miles and 2.75 miles.
The angle lying between the two sides measure 35°.
we are to find the area of the triangle.
We know that the area of a triangle with two adjacent sides of measure 'a' and 'b' units and 'β' be the measure of the angle lying between them is given by
[tex]A=\dfrac{1}{2}ab\sin \beta.[/tex]
Here, a = 2.75 miles, b = 1.32 miles and β = 35°.
Therefore, the total search area, in the form of triangle is given by
[tex]A=\dfrac{1}{2}\times 2.75\times 1.32\times \sin 35^\circ=1.815\times 0.5735=2.08~\textup{mi}^2.[/tex]
Thus, the correct option is (A) 2.08 mi².
Hence, the correct options are (2). A, (3). A.
