Math Problem Statement
Solve for missing sides and angles, Given: C = 6.8 degrees B = 1.9 degrees c = 27
Solution
To solve the triangle, we will determine the missing sides and angles using the given data. Since two angles and are known, we can find the third angle , and then use the Law of Sines to find the missing sides and .
Step 1: Find angle
The sum of the angles in a triangle is . Therefore:
Step 2: Apply the Law of Sines
The Law of Sines states: We know and . First, calculate and .
Then:
I’ll calculate these values. math
Given values
C = 6.8 # in degrees B = 1.9 # in degrees c = 27 # side c
Convert angles to radians for sine calculation
C_rad = math.radians(C) B_rad = math.radians(B)
Find A in degrees
A = 180 - C - B
Convert A to radians
A_rad = math.radians(A)
Calculate sines of angles
sin_C = math.sin(C_rad) sin_B = math.sin(B_rad) sin_A = math.sin(A_rad)
Calculate sides using the Law of Sines
a = (c * sin_A) / sin_C b = (c * sin_B) / sin_C
a, b, AThe missing sides and angle are as follows:
These values were calculated using the Law of Sines. Let me know if you would like detailed steps or have further questions.
Here are 5 related questions for further exploration:
- How does the Law of Sines apply to obtuse triangles?
- What would change if the triangle were a right triangle?
- How can the Law of Cosines be used in this situation?
- Why does the triangle's shape depend on the sum of angles equaling ?
- Can you confirm the side lengths satisfy the triangle inequality?
Tip: Always check the feasibility of triangle side lengths and angles to ensure no input errors.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Triangle Properties
Law of Sines
Formulas
Sum of angles in a triangle: A + B + C = 180°
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
Theorems
Law of Sines
Suitable Grade Level
Grades 10-12
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