Find the geometric mean of the pair of numbers 81 and 4
1 answer:
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1) To find 
we are going to use the Pythagorean equation:
where
and 
are the legs of our triangle. For our picture we can infer that 
and 
, so lets replace those values in our equation to find :
We can conclude that the value of in our triangle is 12.8
2) To find
we are going to use the trigonometric function tangent. Remember that 
. We know that the opposite side of our angle is 8, and its adjacent side is 10, so lets replace those values in our tangent function to find :
Since we need the measure of angle, we are going to take inverse tangent to both sides to find it:
We can conclude that the value of in our triangle is 38.66°
3) Finally, to find
we are going to take advantage of two facts: the sum of the interior angles of a triangle is always 180°, and our triangle is a right one, so one of its sides is 90°. Therefore, 
. Since we already know the value of , lets replace it in our equation and solve for :
We can conclude that the measure of angle is 51.34°
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where
We can conclude that the value of
2) To find
Since we need the measure of angle
We can conclude that the value of
3) Finally, to find
We can conclude that the measure of angle
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