Math Problem Statement
Solution
It seems like you've uploaded two images from a mathematics word problem assignment involving right triangles. Let me help break down what you're working on.
From the images:
-
Right Triangle Properties:
- In the first image, you are asked to find the lengths of the sides of the lower triangle.
- The provided values for the longer leg (48 ft), shorter leg (36 ft), and hypotenuse (60 ft) correspond to a 3-4-5 Pythagorean triple scaled by 12, which fits perfectly since and .
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Second Image:
- The setup involves two adjacent right triangles with a common leg, forming a larger triangle.
- The hypotenuse of the lower triangle is , and the short leg is .
- The hypotenuse of the upper triangle is 21 feet.
The problem is leading towards using the Pythagorean Theorem in both triangles to find the value of . Let me work through the problem for you step by step.
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Math Problem Analysis
Mathematical Concepts
Right Triangles
Pythagorean Theorem
Algebra
Formulas
Pythagorean Theorem: a^2 + b^2 = c^2
Area of Triangle: (1/2) * base * height
Theorems
Pythagorean Theorem
Suitable Grade Level
Grades 9-12
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