Math Problem Statement
θを求めてください
Solution
To solve for the angle in the right triangle shown in the image, we can apply trigonometric relationships.
The right triangle has:
- The opposite side of angle as 2,
- The adjacent side as 1, and
- The hypotenuse as 5.
Using the tangent function, which relates the opposite and adjacent sides:
Now, to find , we can take the arctangent (inverse tangent) of 2:
Let me calculate that for you.The angle is approximately .
Would you like further details on the solution? Here are some related questions:
- How can we verify this result using the sine or cosine functions?
- How would you calculate the other angle in the triangle?
- What would happen if the sides of the triangle were different?
- How does the Pythagorean theorem apply to this problem?
- Can the law of sines or cosines be used to solve this triangle?
Tip: In trigonometry, the tangent function is particularly useful for right triangles when only the opposite and adjacent sides are known.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right-Angle Triangles
Formulas
tan(θ) = opposite/adjacent
θ = arctan(opposite/adjacent)
Theorems
Pythagorean Theorem
Tangent Function
Suitable Grade Level
Grades 9-11
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