Math Problem Statement
solve for length x using trigonometric ratio
Solution
To solve for the length in the right triangle using trigonometric ratios, we can use the tangent function. The tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
In this triangle:
- The angle given is .
- The side opposite this angle is the side with length .
- The side adjacent to this angle is the side with length .
The tangent function is given by:
Substituting the given values:
Now, solve for :
Let's calculate this value.
Thus, the length is approximately units.
Would you like further details, or do you have any questions?
Here are some related questions you might consider:
- How can you use the sine function to find the hypotenuse in this triangle?
- What is the length of the hypotenuse using the sine function?
- Can we use the cosine function to find the length ?
- How would you find the area of this right triangle?
- What is the value of the other non-right angle in this triangle?
- What would be the length of if the angle was instead of ?
- How does the tangent function change as the angle increases?
- How can we verify the length using the Pythagorean theorem?
Tip: It's essential to double-check your trigonometric calculations, especially when working with angles, to ensure accuracy in your results.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right triangle
Formulas
Tangent function
Theorems
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Suitable Grade Level
Grades 9-12
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