Math Problem Statement
Find all sides and angles of the triangle
Solution
The given image shows a right triangle with:
- cm
Step 1: Find
Since is a right triangle, the sum of the angles in a triangle is . Therefore, can be found as:
Step 2: Use trigonometric ratios to find and
- Finding (Hypotenuse):
Using the sine function:
Calculating:
- Finding (Adjacent side to ):
Using the tangent function:
Calculating:
Final Results:
- cm
- cm
Would you like more details or have any questions?
Here are 5 related questions for further exploration:
- How would the triangle's sides change if were larger?
- What is the area of based on the calculated sides?
- Can you use the Pythagorean theorem to verify the side lengths of ?
- How would you find the length of side using the cosine of ?
- What happens to the trigonometric ratios if were given instead of ?
Tip: When working with right triangles, always ensure the angle you reference corresponds to the correct side (opposite, adjacent, or hypotenuse) to use the right trigonometric function.
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Math Problem Analysis
Mathematical Concepts
Geometry
Trigonometry
Formulas
Sine function
Tangent function
Theorems
Sum of angles in a triangle
Suitable Grade Level
Grades 9-12
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