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Answer:
( 36 ) inches^2
Step-by-step explanation:
To find the area of non-geometric shapes we have to divide it into different segment ( image attached below)
Step 1: Area A
= 5 x 2
= 10 inches ^2
Step 2: Area B
= 4 x 4
= 16 inches ^2
Step 3: Area C
= 5 x 2
= 10 inches ^2
Step 4: Total area ( add all)
= ( 10 + 16 + 10 ) inches ^2
= ( 36 ) inches ^ 2
Answer:
There is only one triangle possible
Angles:
A = 112, B = 31.9932, C = 36.0068
Sides:
a = 7, b = 4, c = 4.4384
See the attached image for a visual diagram.
==============================================
Explanation:
Use the law of sines to solve for angle B
sin(A)/a = sin(B)/b
sin(112)/7 = sin(B)/4
0.132454836366684 = sin(B)/4
4*0.132454836366684 = 4*sin(B)/4
0.529819345466736 = sin(B)
sin(B) = 0.529819345466736
arcsin(sin(B)) = arcsin(0.529819345466736)
B = arcsin(0.529819345466736) ... or ... B = 180 - arcsin(0.529819345466736)
B = 31.9932495421859 ... or ... B = 148.006750457814
B = 31.9932 ... or ... B = 148.0068
If B = 31.9932, then C = 180-A-B = 180-112-31.9932 = 36.0068
If B = 148.0068, then C = 180-A-B = 180-112-148.0068 = -80.0068
A negative angle is not possible, so we toss out this value
So only angle B = 31.9932 is possible
--------------------------
Once we know the measure of angle C, we can use that to find side c by using the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = (7)^2 + (4)^2 - 2*(7)*(4)*cos(36.0068)
c^2 = 49 + 16 - 56*0.808947228919362
c^2 = 49 + 16 - 45.3010448194843
c^2 = 19.6989551805157
c = sqrt(19.6989551805157)
c = 4.4383505022154
c = 4.4384
By this point, we're done since we found the remaining missing angles and missing side.
There is only one triangle possible
Angles:
A = 112, B = 31.9932, C = 36.0068
Sides:
a = 7, b = 4, c = 4.4384
See the attached image for a visual diagram.
==============================================
Explanation:
Use the law of sines to solve for angle B
sin(A)/a = sin(B)/b
sin(112)/7 = sin(B)/4
0.132454836366684 = sin(B)/4
4*0.132454836366684 = 4*sin(B)/4
0.529819345466736 = sin(B)
sin(B) = 0.529819345466736
arcsin(sin(B)) = arcsin(0.529819345466736)
B = arcsin(0.529819345466736) ... or ... B = 180 - arcsin(0.529819345466736)
B = 31.9932495421859 ... or ... B = 148.006750457814
B = 31.9932 ... or ... B = 148.0068
If B = 31.9932, then C = 180-A-B = 180-112-31.9932 = 36.0068
If B = 148.0068, then C = 180-A-B = 180-112-148.0068 = -80.0068
A negative angle is not possible, so we toss out this value
So only angle B = 31.9932 is possible
--------------------------
Once we know the measure of angle C, we can use that to find side c by using the law of cosines
c^2 = a^2 + b^2 - 2*a*b*cos(C)
c^2 = (7)^2 + (4)^2 - 2*(7)*(4)*cos(36.0068)
c^2 = 49 + 16 - 56*0.808947228919362
c^2 = 49 + 16 - 45.3010448194843
c^2 = 19.6989551805157
c = sqrt(19.6989551805157)
c = 4.4383505022154
c = 4.4384
By this point, we're done since we found the remaining missing angles and missing side.