Perimeter of the equilateral triangle KLM with vertices K(-2 ,1) and M (10,6) is equal to 39 units.
As given in the question,
Coordinates of vertices K(-2,1) and M(10,6)
KM = 
= 
= 13units
In equilateral triangle KL = LM = KM = 13 units
Perimeter of equilateral triangle KLM = 13 +13 +13
= 39 units
Therefore, perimeter of the equilateral triangle KLM with vertices K(-2 ,1) and M (10,6) is equal to 39 units.
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Answer:
4. $130.50
Step-by-step explanation:
Sorry, but I only know for no.4 which is $130.50.
Explanation: 18 hours is 20 percent more than 15 hours.
So all we have to do is multiply 1.2 to 108.75, since multiplying 1.2 is the equivalent to 20 percent.
Which then is why I get the answer of $130.50.
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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
