Let x = the length of the triangle's hypotenuse
using proportions, this is what the equation looks like:
cross multiply to get:
divide both sides by 45 to get
x=12
The straight edge of the semicircle is 4 units, as this is this the diameter.
The circumference of the full circle is
C = pi*d = pi*4 = 4pi
which is the distance around the full circle (aka circle's perimeter)
So half of this is 4pi/2 = 2pi
Add this onto the straight edge length to get 4+2pi as the exact distance around the entire semicircle. This includes both straight and curved portions.
If you use the approximation pi = 3.14, then 4+2*pi = 4+2*3.14 = 10.28 is the approximate answer. To get a more accurate answer, use more decimal digits in pi.
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In summary,
exact answer in terms of pi is 4+2pi units
approximate answer is roughly 10.28 units (using pi = 3.14)
We will turn the left side into the right side.
Use the identity:
Now use the identity
solved for sin^2 x and for cos^2 x.
I think it is because they are both different differences
Alternate angles - happy to help!
