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10 B 14 A

10 B 14 A

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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### Solving the Right Triangle Below are two diagrams of right triangles that we need to solve. #### Triangle 1: This is a right triangle labeled with vertices A, B, and C. The right angle is at vertex C. - **Side AC (hypotenuse):** 14 units - **Side BC (opposite):** 10 units - **Side AB (adjacent):** (It is not labeled and needs to be solved) To solve for side AB, we use the Pythagorean Theorem: \[ a^2 + b^2 = c^2 \] Here, \( c = 14 \), \( b = 10 \): \[ AB^2 + 10^2 = 14^2 \] \[ AB^2 + 100 = 196 \] \[ AB^2 = 96 \] \[ AB = \sqrt{96} = 4 \sqrt{6} \approx 9.8 \text{ units} \] #### Triangle 2: This triangle is also labeled with vertices A, B, and C. The right angle is at vertex B. - **Side AB (hypotenuse):** (It is not labeled and needs to be solved) - **Side BC (opposite):** 16 units - **Side AC (adjacent):** (It is not labeled and needs to be solved) To solve for the sides AB and AC, we again use the Pythagorean Theorem: Let's assume AC = \( a \) and AB = \( c \): From the right triangle relationship: \[ c^2 = 16^2 + a^2 \] \[ c^2 = 256 + a^2 \] Without additional information, if we are given the length of side AC or the length of side AB, we can substitute back to solve for the missing side. ### Conclusion: Solving for the unknowns in right triangles involves using the Pythagorean Theorem to determine the length of the missing side given information about the other two sides. This method is essential for solving various problems involving right triangles in geometry.
Transcribed Image Text:### Solving the Right Triangle Below are two diagrams of right triangles that we need to solve. #### Triangle 1: This is a right triangle labeled with vertices A, B, and C. The right angle is at vertex C. - **Side AC (hypotenuse):** 14 units - **Side BC (opposite):** 10 units - **Side AB (adjacent):** (It is not labeled and needs to be solved) To solve for side AB, we use the Pythagorean Theorem: \[ a^2 + b^2 = c^2 \] Here, \( c = 14 \), \( b = 10 \): \[ AB^2 + 10^2 = 14^2 \] \[ AB^2 + 100 = 196 \] \[ AB^2 = 96 \] \[ AB = \sqrt{96} = 4 \sqrt{6} \approx 9.8 \text{ units} \] #### Triangle 2: This triangle is also labeled with vertices A, B, and C. The right angle is at vertex B. - **Side AB (hypotenuse):** (It is not labeled and needs to be solved) - **Side BC (opposite):** 16 units - **Side AC (adjacent):** (It is not labeled and needs to be solved) To solve for the sides AB and AC, we again use the Pythagorean Theorem: Let's assume AC = \( a \) and AB = \( c \): From the right triangle relationship: \[ c^2 = 16^2 + a^2 \] \[ c^2 = 256 + a^2 \] Without additional information, if we are given the length of side AC or the length of side AB, we can substitute back to solve for the missing side. ### Conclusion: Solving for the unknowns in right triangles involves using the Pythagorean Theorem to determine the length of the missing side given information about the other two sides. This method is essential for solving various problems involving right triangles in geometry.
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