Math Problem Statement
Solution
The problem in the image is asking for trigonometric ratios based on the triangle provided.
The triangle shows:
- Angle
- (adjacent to )
- (opposite to )
- The hypotenuse , calculated as .
To solve for (the hypotenuse), the Pythagorean theorem is applied:
Where and . Substituting in these values:
So, the hypotenuse .
Trigonometric Ratios for Angle :
-
Sine ():
-
Cosine ():
-
Tangent ():
Let me know if you would like further clarification, more details on any step, or additional related topics explained!
Here are 5 follow-up questions based on this:
- How do you find the trigonometric ratios for angle in this triangle?
- Can you explain why the Pythagorean theorem is valid for right-angled triangles?
- How would the trigonometric values change if and ?
- What is the significance of the sine and cosine values being fractions?
- How can you use trigonometric ratios to find the missing angle ?
Tip:
Always ensure you remember the basic trigonometric identities: sine, cosine, and tangent are defined with respect to the opposite, adjacent, and hypotenuse sides of a right triangle.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangle Ratios
Pythagorean Theorem
Formulas
Pythagorean Theorem: q = √(p² + r²)
Sine: sin(θ) = opposite / hypotenuse
Cosine: cos(θ) = adjacent / hypotenuse
Tangent: tan(θ) = opposite / adjacent
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 8-10
Related Recommendation
Calculating Sides of a Right Triangle Using Trigonometry
Solve Trigonometric Problem: Find Side Lengths in Right Triangle with Given Sine Ratio
Trigonometric Ratios of Right Triangles with Sine, Cosine, and Tangent
Trigonometric Ratios of Right Triangles: Finding sin, cos, and tan
Trigonometric Ratios in Right Triangle Problem