Math Problem Statement
Solution
To find the height of the triangle, we can use trigonometric relationships within the given triangle.
Step-by-step solution:
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Given information:
- The side of the triangle has a length of 34 cm.
- The angle opposite the height is .
- The angle between the given side and the base is .
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Using the sine rule (Law of Sines): In this triangle, the height forms a right triangle with the angle at the bottom right. We can use the sine of the angle to find the height .
From the right triangle:
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Solving for : Using the known value for :
Multiply both sides by 34:
Thus, the height is in its simplest form.
Would you like more details or have any questions?
Related Questions:
- How is the sine rule different from the cosine rule?
- Can we find the other sides of this triangle using trigonometry?
- What is the significance of the angle in this triangle?
- How would the height change if the angle at the bottom right was different?
- Could we solve this using the Law of Cosines instead?
Tip:
Always check if there is a simpler right-triangle approach for problems like this before using more complex laws like sine or cosine rules!
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right-angle triangle
Sine function
Formulas
sin(45°) = h / 34
Theorems
Sine rule
Pythagoras' theorem (implicitly)
Suitable Grade Level
Grades 9-11
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