Math Problem Statement
Solution
Let's analyze the image you provided.
Step 1: Checking if the Triangle is a Right Triangle
The triangle has sides labeled 3, 4, and 5. To determine if this is a right triangle, we can use the Pythagorean Theorem:
Here:
- (one leg),
- (the other leg), and
- (the hypotenuse).
Now, check if the equation holds:
Since the Pythagorean Theorem holds, this is indeed a right triangle.
Step 2: Finding the Trigonometric Ratios
Since it's a right triangle, we can now calculate the sine, cosine, and tangent for angle , where is opposite the side of length 4.
Sine of
Cosine of
Tangent of
Final Answers:
Would you like further details or clarification? Here are some related questions to deepen your understanding:
- How does the Pythagorean Theorem help confirm if a triangle is right-angled?
- What would the sine, cosine, and tangent be for angle ?
- How can you derive the Pythagorean identity from sine and cosine?
- What are the general conditions for a triangle to be classified as a right triangle?
- How can you use trigonometric ratios to find unknown angles or sides in right triangles?
Tip: Always verify the hypotenuse is the longest side when using the Pythagorean Theorem.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Pythagorean Theorem
Formulas
Pythagorean Theorem: a^2 + b^2 = c^2
Sine: sin(B) = opposite / hypotenuse
Cosine: cos(B) = adjacent / hypotenuse
Tangent: tan(B) = opposite / adjacent
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-10
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