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Answer:
B = 34.2°
C = 58.2° or 121.8°
c= 10.6
Step-by-step explanation:
Step 1
Finding c
We calculate c using Pythagoras Theorem
c²= a² + b²
c = √a² + b²
a= 8, b = 7
c = √8² + 7²
c = √64 + 49
c = √(113)
c = 10.630145813
Approximately c = 10.6
Step 2
Find B
We solve this using Sine rule
a/sin A = b/sin B
A = 40°
a = 8
b = 7
Hence,
8/sin 40° = 7/sin B
8 × sin B = sin 40° × 7
sin B = sin 40° × 7/8
B = arc sin (sin 40° × 7/8)
B ≈34.22465°
Approximately = 34.2°
Step 3
We find C
Find B
We solve this using Sine rule
b/sin B = c/sin C
B = 34.2°
b = 7
c = 10.6
C = ?
Hence,
7/sin 34.2° = 10.6/sin C
7 × sin C = sin 34.2 × 10.6
sin C = sin 34.2° × 10.6/7
C = arc sin (sin 34.2° × 10.6/7)
C = arcsin(0.85)
C= 58.211669383
Approximately C = 58.2°
Or = 180 - 58.2
C = 121.8°
Answer:
312π mm^2
Step-by-step explanation:
to find the volume of the figure, you have to calculate the volume of a cone and the volume of a sphere divided it by 2.
The volume of a cone is 1/3 * π * r ^ 2 * h, replacing the information:
V = 1/3 * (6) ^ 2 * (14) = 168π mm^2
The volume of a sphere is 4/3 * π * r ^ 3, replacing the information:
V = 4/3 * π * (6) ^ 3 = 288π mm^2
but since you only have half the sphere
V = 288π / 2 = 144π mm^2
then the total volume is
Vt = 168π + 144π = 312π mm^2
