Question

Solve each problem. Area of a Triangular Lot A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are $52.1 \mathrm{m}$ and $21.3 \mathrm{m}$ and the angle between them is $42.2^{\circ} .$ What is the area of the triangular lot?

Name: Problem 60, Chapter 7: Trigonometry
Uploaded: 2022-10-31T03:14:19-08:00
Channel: Michael Anderson
Description: Solve each problem. Area of a Triangular Lot A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are 52.1 m and 21.3 m and the angle between them is 42.2^∘ . What is the area of the triangular lot?

   Solve each problem.
Area of a Triangular Lot A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are $52.1 \mathrm{m}$ and $21.3 \mathrm{m}$ and the angle between them is $42.2^{\circ} .$ What is the area of the triangular lot?

Trigonometry

Margaret L. Lial,… 11th Edition

Chapter 7, Problem 60

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Solved by Expert Michael Anderson

10/31/2022

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The two sides of the triangle are given as $52.1 \mathrm{m}$ and $21.3 \mathrm{m}$, and the angle between them is $42.2^{\circ}$. Show more…

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Solve each problem. Area of a Triangular Lot A real estate agent wants to find the area of a triangular lot. A surveyor takes measurements and finds that two sides are $52.1 \mathrm{m}$ and $21.3 \mathrm{m}$ and the angle between them is $42.2^{\circ} .$ What is the area of the triangular lot?

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Key Concepts

Trigonometric Functions in Geometry

Trigonometric functions, especially the sine function, play a critical role in relating the angles of a triangle to its side lengths. In the context of triangle area computation, the sine function accounts for the effect of the angle between sides, making it possible to derive the area even when traditional measurements like height are not directly available.

Triangle Area Formula using Sine

This formula calculates the area of a triangle when two sides and their included angle are known. It is expressed as one-half of the product of the two side lengths multiplied by the sine of the included angle, allowing for the area computation without needing to determine the height explicitly.

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