6x + 5x + (x + 16) + (3x - 1) = 360
11x + x + 16 + 3x - 1
15x + 15 = 360
15x = 345
x = 23
6(23) = 138
((23) + 16) = 39
(3(23) - 1) =68
5(23) = 115
138 + 39 + 68 + 115 = 360
5 * 1/4
5/1 * 1/4
5/4
The expression results in an improper fraction.
Answer:
m∠K = 37° and n = 31
Step-by-step explanation:
A lot of math is about matching patterns. Here, the two patterns we want to match are different versions of the same Law of Cosines relation:
- a² = b² +c² -2bc·cos(A)
- k² = 31² +53² -2·31·53·cos(37°)
<h3>Comparison</h3>
Comparing the two equations, we note these correspondences:
Comparing these values to the given information, we see that ...
- KN = c = 53 . . . . . . . . . . matching values 53
- NM = a = k . . . . . . . . . . . matching values k
- KM = b = n = 31 . . . . . . . matching values 31
- ∠K = ∠A = 37° . . . . . . . matching side/angle names
Abby apparently knew that ∠K = 37° and n = 31.
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<em>Additional comment</em>
Side and angle naming for the Law of Sines and the Law of Cosines are as follows. The vertices of the triangle are labeled with single upper-case letters. The side opposite is labeled with the same lower-case letter, or with the two vertices at either end.
Vertex and angle K are opposite side k, also called side NM in this triangle.
The answer is the option b. 1.
Two sides and one angle determine one unique triangle.
If the angle is the between the two sides, you just can use the rule known as SAS, Side Angle Side.
When that is the case you use the cosine rule.
When the known angle is not between the two sides but one of the others, you use sine theorem.
Then in any case when you know two sides and one angle of a triangle the other side and angles are determined, which implies that there is only one possible triangle.
Answer:
b= 26
Step-by-step explanation:
there are 2 triangles
area of the right angles triangle
1/2bh= 1/2 x3 x4 = 6cm²
for the next triangle we use pythagoras theorem to calculate the height
3²+4² = h² = 9+16 = 25
h = √25 =5
1/2bh = 1/2 x 5 x8 = 20
adding the two areas will give the area of the figure = 20 + 6 = 26