Math Problem Statement
Solution
The image shows a right triangle with the following dimensions:
- Opposite side to angle : 41.76
- Adjacent side to angle : 22
- Hypotenuse: 47.2
We can use trigonometric ratios to solve for angle . Since the triangle is a right triangle, we can apply the following relationships:
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Tangent (tan) of an angle is the ratio of the opposite side to the adjacent side:
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To find , take the arctangent (inverse of tangent):
Let me calculate :
Thus, the angle .
Would you like further details or have any questions?
Here are 5 related questions to expand on this:
- What is the sine of angle using the triangle's sides?
- How can we calculate the cosine of angle ?
- Can the Pythagorean theorem verify the given side lengths of the triangle?
- How would you find the area of this right triangle?
- How can we express angle in radians?
Tip: When working with right triangles, the Pythagorean theorem is a reliable way to check the accuracy of the given side lengths.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangles
Inverse Trigonometric Functions
Formulas
tan(θ) = Opposite / Adjacent = 41.76 / 22
θ = tan^(-1)(41.76 / 22)
Theorems
Pythagorean Theorem
Trigonometric Ratios
Suitable Grade Level
Grades 10-12