Math Problem Statement
Solution
To solve the problem, we can use trigonometry since the scenario forms a right triangle.
Step 1: Understand the problem
- Given:
- Length of the tent pole (opposite side):
- Angle between the support rod and the ground:
- We are tasked to calculate the length of the support rod (the hypotenuse).
Step 2: Identify the trigonometric relationship
Since we know the angle and the opposite side and want the hypotenuse, we use the sine function:
Here:
- Opposite =
- Hypotenuse = (the length of the support rod).
Rearranging for :
Step 3: Substitute values
Substitute and opposite = :
Using a calculator to find :
Now calculate :
Step 4: Round the answer
The length of the support rod, rounded to the nearest integer, is:
Final Answer:
The support rod is 254 cm long.
Let me know if you would like me to explain this further or solve a similar problem! Here are 5 related questions:
- How would the problem change if the angle were instead of ?
- How can we calculate the distance of the base of the support rod from the pole?
- What trigonometric function relates the adjacent side and the hypotenuse?
- If the tent pole were taller, say , how would the support rod length change?
- How do you use the cosine rule to find unknown side lengths in triangles?
Tip:
Always check which trigonometric function (sine, cosine, tangent) applies to a triangle problem based on the sides and angles you know.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right Triangles
Sine Function
Formulas
sin(θ) = opposite / hypotenuse
L = opposite / sin(θ)
Theorems
Basic Trigonometric Ratios
Suitable Grade Level
Grades 9-10
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