Answer:
• c = √89 ≈ 9.434
• A = arcsin(8/√89) ≈ 57.995°
• B = arcsin(5/√89) ≈ 32.005°
Step-by-step explanation:
By the law of cosines, ...
c² = a² + b² -2ab·cos(C)
Since c=90°, cos(C) = 0 and this reduces to the Pythagorean theorem for this right triangle.
c = √(8² +5²) = √89 ≈ 9.434
Then by the law of sines (or the definition of the sine of an angle), ...
sin(A) = a/c·sin(C) = a/c = 8/√89
A = arcsin(8/√89) ≈ 57.995°
sin(B) = b/c·sin(C) = b/c = 5/√89
B = arcsin(5/√89) ≈ 32.005°
So it's actually 0.36363636... with the 36 repeating, right?
<span>Here's a technique for converting repeating decimals to fractions: </span>
<span>N = 0.3636363636... </span>
<span>100N = 36.36363636... </span>
<span>This means 100N - N = (36.363636...) - (0.36363636...). This simplifies to 99N = 36, because the "0.36363636..." parts of both numbers on the right cancel each other out. </span>
<span>Solving this for N gives </span>
<span>N = 36/99, or 4/11 </span>
<span>If you take a calculator (or use long division) and divide 4 by 11, you'll see that it's 0.36363636...</span>
10.68 each for the 2 same length sides. The total of the 5 sides is 45.56 less the 3 sides which total 24.2 leaves 21.36 remaining for the 2 equal length sides. So divide 21.36 by 2 = 10.68
(45.56 - 24.2)/2 = 10.68
Answer:
There are a few solutions because there are some fractions and decimals between 8 and 10
Step-by-step explanation:
Let the unknown number be 'x'
If the number is greater than 8 and the same number is less than 10, this can be expressed as;
x>8 and x < 10
Note that if x>8, then 8<x
The resulting inequalities are now;
8<x and x<10
Combining both inequalities we have: 8<x<10
Since the inequality didn't tell us that the variable 'x' is equal to 8 and 10, this means that our solution falls between 8 and 10 and the value of integer that falls within this range is 9. Other values that falls within this range are decimals and fractions.
Therefore it can be concluded that there are a few solutions because there are some fractions and decimals between 8 and 10
That is the exact representation of the constant π. By definition:
π=C/d, where C is the circumference of a circle and d is the diameter.
