Step-by-step explanation:
Use distance formula to find the lengths of the sides.
a = √((8 − (-7))² + (-6 − (-4))²) = √229
b = √((8 − (-8))² + (-6 − (-5))²) = √257
c = √((-7 − (-8))² + (-4 − (-5))²) = √2
Use law of cosine to find one of the angles.
c² = a² + b² − 2ab cos C
(√2)² = (√229)² + (√257)² − 2(√229)(√257) cos C
2 = 229 + 257 − 2√58853 cos C
cos C = 242/√58853
C = 4.018°
To find the second angle, either use law of sines, or use law of cosine again. Using law of cosine:
b² = a² + c² − 2ac cos B
(√257)² = (√229)² + (√2)² − 2(√229)(√2) cos B
257 = 229 + 2 − 2√458 cos B
cos B = -13/√458
B = 127.405°
Finally, find the third angle using sum of angles of a triangle, or law of sines, or law of cosine. Using law of cosine:
a² = b² + c² − 2bc cos A
(√229)² = (√257)² + (√2)² − 2(√257)(√2) cos A
229 = 257 + 2 − 2√514 cos A
cos A = 15/√514
A = 48.576°
Answer
Find out the what fraction of the sandcastle did they build together .
To prove
Let us assume that the fraction of the sandcastle they build together be x .
As given
Than the equation becomes
L.C .M of (3,7) = 21
solving
Therefore the fraction of the sandcastle did they build together be
Hence proved
Multiply the bracket by 5
10x+25= 4x-7
10x-4x+25= 4x-4x-7
6x+25= -7
6x+25-25= -7-25
6x= -32
Divide by 6 for 6x and -32
6x/6= -32/6
x= -32/6
divide by 2 for -32/6
x= -16/3
Answer is -16/3 ( improper fraction) or -5 1/3 ( mixed number)
Answer:
All answers are correct.
Step-by-step explanation:
