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.
Answer:
2.4 cm
Step-by-step explanation:
The formula we would use
S = rθ
Where S = Arc length
θ = central angle in radians
r = radius of the circle or length of the radius.
From the question, we can see that if
If C = a point on circle A
The Segment BC = The arc length of the circle = 12cm
∠BAC = central angle in radians = 5 radians.
Since, S = rθ,
Length of the radius = S/θ
= 12cm/5 radians
Length of the radius = 2.4 cm
X+7x=180
8x=180
x= 22.5
the larger angle is 157.5 degrees.
the angle c is 90°, it is a right triangle. (you see from the picture).
the sum of the interior angles are 180° (in all triangles)
so
180 - 90 - 29 =
61° (angle A)
----------------------
90 + 61 + 29 = 180°
