Find the area of each triangle using the formula 𝒜=(1)/(2) b h, and then verify that the formula

Name: Problem 71, Chapter 8: College Algebra and Trigonometry
Uploaded: 2021-09-09T00:28:20-08:00
Duration: 1 min 36 s
Channel: Christy Galilei
Description: Find the area of each triangle using the formula 𝒜=(1)/(2) b h, and then verify that the formula 𝒜=(1)/(2) a b sinC gives the same result.

step 1 Let's find the area of this triangle using area equals one -half base times height. So one -half

Question

Find the area of each triangle using the formula $\mathcal{A}=\frac{1}{2} b h,$ and then verify that the formula $ \mathcal{A}=\frac{1}{2} a b \sin C$ gives the same result.

   Find the area of each triangle using the formula $\mathcal{A}=\frac{1}{2} b h,$ and then verify that the formula $ \mathcal{A}=\frac{1}{2} a b \sin C$ gives the same result.

College Algebra and Trigonometry

Margaret L. Lial,… 7th Edition

Chapter 8, Problem 71

Instant Answer

Solved by Expert Christy Galilei

09/09/2021

Step 1

Here, the base (b) is 1 and the height (h) is $\sqrt{3}$. So, the area is $\frac{1}{2} \times 1 \times \sqrt{3} = \frac{\sqrt{3}}{2}$. Show more…

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Find the area of each triangle using the formula $\mathcal{A}=\frac{1}{2} b h,$ and then verify that the formula $ \mathcal{A}=\frac{1}{2} a b \sin C$ gives the same result.

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Key Concepts

Triangle Area Using Two Sides and Included Angle

This concept calculates the area of a triangle when two sides and the angle between them are known. The formula, area = 1/2 × a × b × sin(C), uses trigonometric principles, specifically the sine of the included angle, to find the effective height relative to the base. This method is particularly useful when the height is not easily measurable, but the side lengths and their contained angle are available.

Triangle Area Using Base and Height

This concept involves calculating the area of a triangle by identifying one side as the base and measuring the perpendicular distance from this base to the opposite vertex, known as the height. The formula, area = 1/2 × base × height, is a fundamental geometric method used to determine the area enclosed by any triangle, provided these two dimensions are known.

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