Math Problem Statement
Solution
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Problem Statement
The image shows two triangles. The left triangle is a right-angled triangle with sides labeled as follows:
- The side opposite the right angle is labeled cm.
- One leg is labeled cm.
- The other leg is labeled .
The right triangle is a non-right-angled triangle labeled as follows:
- One side is labeled cm.
- Another side is labeled cm.
- The angle between these sides is labeled .
Task
- For the left triangle, we need to find the length of the unknown side .
- For the right triangle, we need to find the length of the third side using the given angle.
Step-by-Step Solution
-
For the Left Triangle (Right-Angled):
Since it's a right-angled triangle, we can use the Pythagorean Theorem: Given cm and cm, we substitute into the equation:
-
For the Right Triangle (Non-Right-Angled):
We use the Cosine Rule to find the unknown side : Given cm, cm, and , we substitute into the equation:
Summary of Answers:
- For the left triangle, cm.
- For the right triangle, cm.
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Related Questions
- How would you find the area of each triangle?
- What is the perimeter of the right triangle after finding all sides?
- How does the Cosine Rule change if the angle is obtuse?
- Can you calculate the angles of the left triangle using trigonometric ratios?
- What happens if the angle in the right triangle was given as ?
Tip
Always remember to check whether a triangle is right-angled before choosing the appropriate theorem or formula for solving side lengths.
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Math Problem Analysis
Mathematical Concepts
Trigonometry
Geometry
Pythagorean Theorem
Cosine Rule
Formulas
Pythagorean Theorem: c^2 = a^2 + b^2
Cosine Rule: a^2 = b^2 + c^2 - 2bc * cos(α)
Theorems
Pythagorean Theorem
Cosine Rule
Suitable Grade Level
Grades 8-10