WILL GIVE BRAINLIEST AND 30 POINTS!
2 answers:
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Answer:
<A = 90°, <B = 71.6° <C = 18.4°
Step-by-step explanation:
Given the vertices of a △ABC to be A(−1, 6), B(2, 10), and C(7, −2)
Before we can get each angle of the triangle, we need to get its sides first.
Using the formula fie finding the distance between two points
D = √(x2-x1)²+(y2-y1)²
For side AB:
Given A(−1, 6), B(2, 10)
AB = √{2-(-1)}²+(10-6)²
AB =√3²+4²
AB = √25
AB = 5
For side AC:
Given A(-1,6) and C(7, −2)
AC = √{7-(-1)}²+(-2-6)²
AC = √8²+8²
AC = √128
AC = √64×2
AC = 8√2
For side BC:
Given B(2,10) and C(7, −2)
BC = √(7-2)²+(-2-10)²
BC = √5²+12²
BC = √25+144
BC = √169
BC = 13
First we need to get theta using cosine rule
|AC|² = |AB|+|BC| - 2|AB||AC| cos theta
(8√2)² = 5²+13²-2(5)(13)cos theta
128 = 169-130costheta
128-169 = -130costheta
-41= -130costheta
Costheta = -41/-130
Cos theta = 0.315
theta = arccos 0.315
theta = 71.64°
<B = 71.6°
Using sine rule to get <A,
BC/sin A = AC/sinB
13/sinA = 8√2/sin71.6°
8√2sinA = 13sin71.6°
SinA = 12.34/8√2
SinA = 1.09°
A = arcsin1
<A = 90.0°
<C = 180°-(71.6+90)
< C = 180-161.6
<C = 18.4°
Answer:
Therefore the value of k = 6.
Step-by-step explanation:
Given:
LN = m
NM = l
OM = k
NO = 4
LO = 8
LM = 8 + k and
Δ LNM ,Δ LON and Δ MON are right Triangle.
To Find :
Om = k = ?
Solution:
In Right angle Triangle By Pythagoras Theorem we have,
So, In Right angle Triangle Δ LON we have,
LN² = ON² + OL²
m² = 4² + 8²
m² = 80 ............( 1 )
Now in Right angle Triangle Δ MON we have,
MN² = ON² + MO²
l² = 4² + k² ....................( 2 )
Now In Right angle Triangle Δ LNM we have,
LM² = LN² + MN²
(8 + k)² = m² + l² .................( 3 )
Substituting equation 1 and equation 2 in equation 3
(8+k)² = 80 + 4² + k²
Applying (A+B)² = A² +2AB + B² we get
Therefore the value of k = 6.
Answer:
60/220
Step-by-step explanation:
we use combination,
then, all divided by,