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If varies directly as
, then there is some constant
for which
Similarly, there is some constant such that
Given that when
, we have
Now when , we get
The sum of the lengths of two legs of the 30°-60°-90° right triangle is 6.69 centimeters. Using the ratio of sides for the 30°-60°-90° triangle, the sum is calculated.
<h3>What is the ratio of sides for the 30°-60°-90° triangle?</h3>The ratio for the 30°-60°-90° triangle is 1:√3:2 or x:x√3:2x
where x corresponds to the length opposite the 30° angle and x√3 is opposite of the 60° angle and 2x is opposite to the 90° angle.
<h3 /><h3>Calculation:</h3>It is given that the triangle is a right triangle with angles 30°-60°-90°
For such a triangle, the ratio of side lengths is x: x:2x
we have the length of the hypotenuse is
So, 2x =
⇒ x =
So,
the other length of the other leg is x√3 = √6 × √3 = 3 √2
Then, the sum of these two legs = √6 + 3√2 = 6.69 centimeters.
Learn more about the ratio of sides of a 30°-60°-90° triangle here:
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The graph of is a horizontal line. So the area under
on [0, 8] is equal to the area of a rectangle with length 8 and height 2, or 16.
The graph of is the upper half of a circle with radius
. It's symmetric about
, so on the interval [0, 8], we're considering a quarter of the circle. The area of such a sector is
.
Then use the fact that the definite integral is distributive over sums, meaning