Math Problem Statement
Solution
To solve the given problem, let's analyze the triangle and find the values of , , and using trigonometric identities.
Step 1: Identify the sides of the triangle
The right triangle shows:
- Opposite side to :
- Adjacent side to : Unknown for now
- Hypotenuse:
We can find the adjacent side using the Pythagorean theorem: Let's calculate it:
Now, we have:
- Opposite side:
- Adjacent side:
- Hypotenuse:
Step 2: Find , , and
Final answers:
Would you like a more detailed explanation or have any questions?
Related Questions:
- How do you find the remaining trigonometric ratios (, , ) for this triangle?
- What is the value of in degrees or radians?
- How does the Pythagorean identity relate to this triangle?
- How can you determine if given only ?
- Why is the reciprocal of ?
Tip:
In right triangles, always start with the Pythagorean theorem to find missing sides, which helps in determining all trigonometric ratios accurately.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangles
Formulas
sin(θ) = opposite / hypotenuse
csc(θ) = 1 / sin(θ)
cot(θ) = adjacent / opposite
Pythagorean Theorem: a^2 + b^2 = c^2
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-12
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