Math Problem Statement
Solution
The question involves finding the length of side in a right triangle. The given information is as follows:
- One angle measures ,
- The adjacent side to this angle is 8 cm,
- The side is the opposite side of the triangle, corresponding to the given angle.
To solve for , we can use the trigonometric function tangent () because we have the opposite side and adjacent side.
The formula for tangent is:
Substituting the known values:
Solving for :
Let me calculate the value of .import math
Given values
angle_degrees = 54 adjacent_side = 8
Convert angle to radians for the math.tan function
angle_radians = math.radians(angle_degrees)
Calculate the length of the opposite side (z)
z = adjacent_side * math.tan(angle_radians) zThe value of is approximately cm, rounded to one decimal place.
Would you like more details on the steps, or do you have any further questions?
Here are some related questions to explore:
- How can sine and cosine be used in this triangle to find other side lengths?
- What are the different trigonometric ratios in a right triangle?
- How would the calculation change if a different angle was given instead of 54°?
- Can you use the Pythagorean theorem here, and if so, how?
- What are the common mistakes when using trigonometric functions?
Tip: Always ensure that your calculator is in the correct mode (degrees or radians) when solving trigonometric problems.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Right-Angle Triangle
Tangent Function
Formulas
tan(θ) = opposite / adjacent
Theorems
Trigonometric Ratios in Right Triangles
Suitable Grade Level
Grades 9-10
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