Question

Find the area of each of the given triangles. Round anstwers to four decimal places.

   Find the area of each of the given triangles. Round anstwers to four decimal places.

Precalculus : Building Concepts and Connections

Precalculus : Building Concepts and Connections

Revathi Narasimhan 1st Edition

Chapter 7, Problem 26

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Solved by Expert Ramzi Deek

05/06/2020

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The formula is $\frac{1}{2}ab\sin C$ where $a$ and $b$ are the sides and $C$ is the included angle. Show more…

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Find the area of each of the given triangles. Round anstwers to four decimal places.

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Key Concepts

Triangle Area Calculation

This concept involves determining the size of a triangle's surface, which can be done using various formulas depending on what measurements are provided. Common methods include using the base and height, Heron’s formula when all side lengths are known, or trigonometric formulas when an angle and two sides are provided.

Heron’s Formula

Heron’s formula is used to calculate the area of a triangle when all three side lengths are known. It involves computing the semiperimeter of the triangle and then finding the square root of the product of the semiperimeter and its differences with each side, providing a way to determine area without needing to know the height.

Trigonometric Area Formula

This approach calculates the area using two sides and the sine of the included angle. The formula, (1/2)ab sin(C), is particularly useful when the height of the triangle is not readily available, leveraging the relationship between side lengths and angles in a triangle.

Rounding

Rounding is the process of approximating a number to a specified degree of precision. In this context, answers must be rounded to four decimal places, ensuring consistency and clarity in the final numerical results.

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