C 136 is the correct answer
Triangle LMN has two sides that are of the same size, therefore, triangle LMN is described as: isosceles triangle.
<h3>What is an Isosceles Triangle?</h3>
A triangle with two equal sides and two equal base angles is described as an isosceles triangle.
<h3>What is the Distance Formula?</h3>
The formula for finding the distance between two coordinate points is called the distance formula, and it is expressed as:
.
Given the vertices of the angles of triangle LMN as:
- L(-2, 4),
- M(3, 2),
- N(1,-3)
Use the distance formula to find the length of each side of the triangle.
LM = √[(3−(−2))² + (2−4)²]
LM = √[(5)² + (−2)²]
LM = √29 units
MN = √[(3−1)² + (2−(−3))]²
MN = √29 units
LN = √[(−2−1)² + (4−(−3))²]
LN = √(−3)² + (7)²]
LN = √(9 + 49)
LN = √58 units
Isosceles triangles have two equal sides. Triangle LMN has two sides that are of the same size, therefore, triangle LMN is described as: isosceles triangle.
Learn more about isosceles triangle on:
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32 3/4-12 1/2
32 3/4-12 2/4
20 1/4
The total arc length around a circle is 360 degrees. So, these 3 arc with expressions given will all add up to 360.
(-2 + 8x) + (10x + 10) + (10x - 12) = 360
28x - 4 = 360
28x = 364
x = 13
Now that we know the value of x, we can plug that value into the expression for arc LM and solve for the measure.
LM = 10x - 12
LM = 10(13) - 12
LM = 118 degrees
Hope this helps! :)
We can use the Sine Law:
a / sin A = b / sin B
16 / sin 22° = 25 / sin B
16 / 0.3746 = 25 / sin B
sin B = 25 · 0.3746 / 16
sin B = 0.5853
∠B = sin^(-1) 0.5853
∠B = 35.83° ≈ 35.8°
Answer: b. 35.8°