Math Problem Statement
Solution
To find the length of in this right triangle using trigonometric ratios, we can apply the tangent function because we have the angle and the adjacent side (9 m). In a right triangle, the tangent of an angle is defined as:
For this problem:
- The angle is .
- The adjacent side is 9 m.
- The opposite side is .
Step-by-Step Solution
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Set up the equation using the tangent function:
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Solve for by multiplying both sides by 9:
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Calculate :
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Substitute and solve:
Answer
The length of is approximately 4.79 m.
Would you like more details on this solution or have any questions?
Here are 5 related questions for further practice:
- What trigonometric ratio would you use if you were given the opposite side and needed to find the hypotenuse?
- How would you calculate the adjacent side if you only knew the hypotenuse and the angle?
- If the angle were changed to , what would the value of be?
- How would you find the length of the hypotenuse if you only had the adjacent side and the angle?
- What are the definitions of sine, cosine, and tangent in a right triangle?
Tip: Remember that tangent relates the opposite side to the adjacent side, which is especially useful in right triangles when you don’t have the hypotenuse.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangle Ratios
Tangent Function
Formulas
tan(angle) = opposite / adjacent
Theorems
Trigonometric Ratios in Right Triangles
Suitable Grade Level
Grades 8-10
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