Math Problem Statement
In ΔDEF, e = 1.8 inches, mm∠F=104° and mm∠D=52°. Find the length of f, to the nearest 10th of an inch.
Solution
In triangle , we know:
- Side inches,
- ,
- .
To find side , let's proceed with the following steps:
Step 1: Calculate
Since the sum of angles in a triangle is ,
Step 2: Use the Law of Sines
The Law of Sines states:
Rearrange to solve for :
Substitute the values:
Step 3: Calculate (using approximate sine values)
Using approximate values, and ,
Answer:
The length of is approximately 0.9 inches to the nearest tenth.
Would you like more details on any of the steps?
Here are some additional questions to deepen understanding:
- How would the calculation change if angle were an acute angle?
- What if side were doubled? How would that affect ?
- How would using the Law of Cosines help in a scenario where we have different known values?
- Can we solve for in the triangle, given the current information?
- How does changing angle impact the overall shape and measurements of the triangle?
Tip: Remember that the Law of Sines is particularly useful when you know two angles and one side or two sides and a non-included angle.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Triangle Properties
Angle Sum in Triangle
Law of Sines
Formulas
m∠E = 180° - m∠F - m∠D
Law of Sines: e / sin(D) = f / sin(E)
f = e * (sin(E) / sin(D))
Theorems
Law of Sines
Triangle Angle Sum Theorem
Suitable Grade Level
Grades 10-12
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