Podcast
Questions and Answers
What type of triangles are discussed in the content?
What type of triangles are discussed in the content?
The content includes an explanation of finding missing sides of acute triangles.
The content includes an explanation of finding missing sides of acute triangles.
True
What is the main focus of the content related to acute triangles?
What is the main focus of the content related to acute triangles?
Finding the missing base.
In geometry, an acute triangle has all angles measuring less than ___ degrees.
In geometry, an acute triangle has all angles measuring less than ___ degrees.
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Match the following concepts with their descriptions:
Match the following concepts with their descriptions:
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Study Notes
Finding the Missing Base of an Acute Triangle
- An acute triangle has three angles, each measuring less than 90 degrees.
- The base of a triangle is any one of its sides. It's often important to identify the height for calculations.
- If a triangle's height and area are known, the base can be calculated.
Formulas and Methods
- Formula: Area = (1/2) * base * height
- Steps:
- Identify the known values (area, height).
- Substitute the known values into the formula.
- Solve the equation for the unknown base.
- Example Problem 1:
- Given area = 18 square units, height = 6 units
- Area = (1/2) * base * height
- 18 = (1/2) * base * 6
- 18 = 3 * base
- Base = 6 units
Practice Problems
- Problem 1: An acute triangle has an area of 24 square centimeters and a height of 8 centimeters. What is the length of its base?
- Problem 2: Another acute triangle has an area of 36 square meters and a height of 9 meters. What is the length of its base?
- Problem 3: Calculate the base of an acute triangle if its height is 12 inches and the area is 60 square inches.
Summary
- To find the missing base of an acute triangle given its area and height, use the area formula: Area = (1/2) * base * height.
- Substitute the known values into the equation, then solve for the unknown base.
Explanation
- Understanding the relationship between area, base, and height in a triangle is crucial.
- The height of a triangle is the perpendicular distance from the base to the opposite vertex.
- Practice problems provide opportunities to apply the formula in different context.
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Description
This quiz focuses on calculating the base of an acute triangle using the area and height. You will explore formulas and methods essential for solving problems related to triangle geometry. Practice various examples to enhance your understanding of triangle dimensions.
