Given data:
The first side of the triangle is p=13 inches.
The second side of the triangle is q=18 inches.
The third side of the triangle is r= 12 inches.
The semi-perimeter is,
The expression for the area of the triangle is,
![\begin{gathered} A=\sqrt[]{s(s-p)(s-q)(s-r)_{}} \\ =\sqrt[]{21.5\text{ in(21.5 in-13 in)(21.5 in-18 in)(21.5 in-12 in)}} \\ =\sqrt[]{(21.5\text{ in)(8.5 in)(3.5 in)(9.5 in)}} \\ =77.95in^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D%5Csqrt%5B%5D%7Bs%28s-p%29%28s-q%29%28s-r%29_%7B%7D%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B21.5%5Ctext%7B%20in%2821.5%20in-13%20in%29%2821.5%20in-18%20in%29%2821.5%20in-12%20in%29%7D%7D%20%5C%5C%20%3D%5Csqrt%5B%5D%7B%2821.5%5Ctext%7B%20in%29%288.5%20in%29%283.5%20in%29%289.5%20in%29%7D%7D%20%5C%5C%20%3D77.95in%5E2%20%5Cend%7Bgathered%7D)
Thus, the area of the given triangle is 77.95 sq-inches.
AO = 21
BC = 14
OC = radius of the circle = AO = 21
∴ OB = OC + CB = 21 + 14 = 35
<span>Line AB is tangent to circle O at A</span>
∴ AB is perpendicular to AO
∴ Δ OAB is a right triangle at A
Applying Pythagorean theorem
∴ OB² = AO² + AB²
∴ AB² = OB² - AO² = 35² - 21² = 1225 - 441 = 784
∴ AB = √784 = 28
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Answer:
C.
Step-by-step explanation:
x is bisecting the baseline (cutting it in 2 halves of 6).
the third angle in the main overall triangle is 60 degrees.
remember, all angles in a triangle always add up to 180 degrees.
so, 180 - 60 - 60 = 60.
that means that all 3 angles are of equal size (60). and that means that all 3 sides must have the same length.
=> y = 12
and now using Pythagoras to calculate the height (x) of the triangle :
y² = x² + 6² (remember, this side is only half the baseline)
12² = x² + 6²
144 = x² + 36
x² = 108
x = sqrt(108) = sqrt(36×3) = 6×sqrt(3)
It will take him 10 because 125*10 is 1250(12.50)
To find scale factor you first must find two corresponding sides. then divide one by the other. note that if you divide the smaller side by the larger you will get a number less that one and if you divide the larger side by the smaller side you will get a number greater than one.
