Math Problem Statement
Solution
The problem requires solving a right triangle by finding all missing sides and angles. The triangle has the following given information:
- Angle
- Angle (since the two angles are complementary in a right triangle)
- Side (adjacent side to and opposite to ).
We need to find:
- Hypotenuse ().
- Opposite side to ().
Step-by-Step Solution:
-
Find (opposite side to ): Using the tangent function: Rearrange to find :
-
Find (the hypotenuse): Using the cosine function: Rearrange to find :
-
Verify the angles: Since this is a right triangle, the angles add up to :
Final Answer:
- Angles are correct (, ).
Let me know if you’d like a more detailed explanation for any step!
Related Questions:
- How can you verify the sides using the Pythagorean theorem?
- What are some real-life applications of solving right triangles?
- How would the solution change if were ?
- Why is the tangent function helpful for finding the opposite side?
- How does the cosine function relate to the hypotenuse?
Tip: Always double-check trigonometric values using a calculator or table for accuracy!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangle
Angles
Formulas
tan(A) = opposite/adjacent
cos(A) = adjacent/hypotenuse
Theorems
Pythagorean Theorem
Trigonometric Ratios
Suitable Grade Level
Grades 10-12
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