Answer:
0,0
Step-by-step explanation:
Answer:
mAB = 49
mABC = 253
mBAC= 156
mACB = 311
Step-by-step explanation:
Answer:
44.47 cm² (nearest hundredth)
Step-by-step explanation:
Area of ΔABC = 1/2 x base x height
⇒ 21 = 1/2 x 7 x BC
⇒ BC = 6 cm
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
⇒ AB² + BC² = AC²
⇒ 7² + 6² = AC²
⇒ AC² = 85
⇒ AC = √85 cm
Cosine rule to find length AD:
c² = a² + b² - 2 ab cosC
⇒ DC² = AD² + AC² - 2(AD)(AC)cos(DAC)
⇒ 9.2² = AD² + (√85)² - 2(AD)(√85)cos 73°
⇒ AD² - 5.39106...AD + 0.36 = 0
⇒ AD = 5.323442445, 0.06762541414
⇒ AD = 5.323442445
Area of a triangle ADC: (1/2)absinC
(where a and b are adjacent sides and C is the angle between them)
⇒ area = (1/2) × AC × AD × sin(DAC)
⇒ area = (1/2) × √85 × 5.323442445 × sin(73°)
⇒ area =23.4675821... cm²
Area of quadrilateral = area of ΔABC + area of ΔADC
= 21 + 23.4675821...
= 44.47 cm² (nearest hundredth)
Answer:
--- small circle
--- big circle
Step-by-step explanation:
Given
-- sum of areas
Required
The radius of the larger circle
Area is calculated as;
For the smaller circle, we have:
For the big, we have
The sum of both is:
Substitute:
Substitute
Factorize
![80\pi = \pi[ r^2 + 4r^2]](https://tex.z-dn.net/?f=80%5Cpi%20%3D%20%5Cpi%5B%20r%5E2%20%2B%204r%5E2%5D)
![80\pi = \pi[ 5r^2]](https://tex.z-dn.net/?f=80%5Cpi%20%3D%20%5Cpi%5B%205r%5E2%5D)
Divide both sides by 
Divide both sides by 5
Take square roots of both sides
The radius of the larger circle is:
