Answer:
The simplest form of the fraction 
is 
.
i.e.
Step-by-step explanation:
Here are some simple observations regarding how to reduce a fraction into simpler terms:
- A fraction is reduced to lowest or simplest terms by finding an equivalent fraction in which the numerator and denominator are as small as possible.
- In order to reduce a fraction to lowest or simplest terms, divide the numerator and denominator by their (GCF). Note that (GCF) is also called Greatest Common Factor .
So, lets take a sample fraction and reduce into simpler terms.
Considering the fraction
so
Therefore, the simplest form of the fraction is .
i.e.
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
The answer would be<span>27 * 3/2 = 40.5</span>
Answer:
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Step-by-step explanation:
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Answer: 30^2 * pi = 2827.43.
