What is the value of x in the parallelogram if two corners are 60 degrees
1 answer:
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Given:
Composite figure made of cylinder and two spheres.
To find:
The volume of the composite solid.
Solution:
Radius = 2 in
The value of π = 3.14
<u>Volume of sphere:</u>
Volume of a sphere is 33.49 in³
Volume of two spheres = 2 × 33.49 = 66.98 in³
Radius of cylinder = 2 in
Height of cylinder = 8 - 2 - 2 = 4 in
<u>Volume of cylinder:</u>
V = 3.14 × 2² × 4
V = 50.24
Volume of cylinder = 50.24 in³
Volume of composite solid = Volume of two spheres + Volume of cylinder
= 66.98 in³ + 50.24 in³
= 117.2 in³
The volume of the composite solid is 117.2 in³.
Answer: 17) 41.0° 18) 60.8° 19) 36.0° 20) 19.7°
<u>Step-by-step explanation:</u>
Law of Cosines: a² = b² + c² - 2bc · cos A
b² = a² + c² - 2ac · cos B
c² = a² + b² - 2ab · cos C
17) a = 29, b = 13, c = 21, C = ???
c² = a² + b² - 2ab · cos C
21² = 29² + 13² - 2(29)(13) · cos C
441 = 841 + 169 - 754 cos C
441 = 1010 - 754 cos C
-569 = -754 cos C
41.0° = C
18) a = 29.3, b = 25.7, c = 16.8, B = ???
b² = a² + c² - 2ac · cos B
25.7² = 29.3² + 16.8² - 2(29.3)(16.8) · cos B
660.49 = 858.49 + 282.24 - 984.48 cos B
660.49 = 1140.73 - 984.48 cos B
-480.24 = -984.48 cos B
60.8° = B
19) a = 12, b = 19, c = 11, A = ???
a² = b² + c² - 2bc · cos A
12² = 19² + 11² - 2(19)(11) · cos A
144 = 361 + 121 - 418 cos A
144 = 482 - 418 cos A
-338 = -418 cos A
36.0° = A
20) a = 10, b = 9, c = 18, A = ???
a² = b² + c² - 2bc · cos A
100² = 9² + 18² - 2(9)(18) · cos A
100 = 81 + 324 - 324 cos A
100 = 405 - 324 cos A
-305 = -324 cos A
19.7° = A