Answer:
1350
units²
Step-by-step explanation:
The regular hexagon consists of 6 equiangular triangles
The area (A) of a equilateral triangle is calculated as
A = 
( s is the side length )
Here s = 30 , then
A = 
= 
= 225 units²
Thus the area of the regular hexagon is
area = 6 × 225
= 1350 units² ← exact value
≈ 2338.3 units² ( to 1 dec. place )
Answer:
8 percent loss
Step-by-step explanation:
The question is find the height of the tree, given that at two points 65 feet apart on the same side of the tree and in line with it, the angles of elevaton of the top of the tree are 21° 19' and 16°20'.
1) Convert the angles to decimal form:
19' * 1°/60' = 0.32° => 21° 19' = 21.32°
20' * 1°/60' = 0.33° => 16° 20' = 16.33°
2) Deduce the trigonometric ratios from the verbal information.
You can form a triangle with
- horizontal leg x + 65 feet
- elevation angle 16.33°
- vertical leg height of the tree, h
=> trigonometric ratio: tan (16.33) = h /( x + 65) => h = (x+65) * tan(16.33)
You can form a second triangle with:
- horizontal leg x
- elevation angle 21.32°
- vertical leg height of the tree, h
=> trigonometric ratio: tan(21.32) = h / x => h = x * tan(21.32)
Now equal the two expressions for h:
(x+65)*tan(16.33) = x*tan(21.32)
=> x*tan(16.33) + 65*tan(16.33) = x*tan(21.32)
=> x*tan(21.32) - x*tan(16.33) = 65*tan(16.33)
=> x = 65*tan(16.33) / [ tan(21.32) - tan(16.33) ] = 195.73 feet
=> h = 195.73 * tan(21.32) = 76.39 feet.
Answer: 76.39 feet
answer:
2.5 or 2 1/2
work:
4(joshuas friends)+1(joshua)=5
5×1/2=5/2
5/2= 2.5
Answer:
f(-5)=28
Step-by-step explanation:
f(x)=x²-2x-7
f(-5) means that we have to replace x by -5.
f(-5)=(-5)²-2(-5)-7=25+10-7=25+3=28
