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

Name: Problem 50, Chapter 7: Trigonometry
Uploaded: 2022-10-31T03:04:48-08:00
Channel: Michael Anderson
Description: Find the area of each triangle using the formula 𝒜=(1)/(2) b h, and then verify that the for. mula 𝒜=(1)/(2) a b sinC gives the same result. (Angle can't copy)

step 1 Okay, in this one, they want you to verify that the formula from geometry, one -half, base, time

Question

Find the area of each triangle using the formula $\mathscr{A}=\frac{1}{2} b h,$ and then verify that the for. mula $\mathscr{A}=\frac{1}{2} a b \sin C$ gives the same result. (Angle can't copy)

   Find the area of each triangle using the formula $\mathscr{A}=\frac{1}{2} b h,$ and then verify that the for. mula $\mathscr{A}=\frac{1}{2} a b \sin C$ gives the same result.
(Angle can't copy)

Trigonometry

Margaret L. Lial,… 11th Edition

Chapter 7, Problem 50

Instant Answer

Solved by Expert Michael Anderson

10/31/2022

Step 1

Here, the base $b$ is 2 and the height $h$ is 1. So, we substitute these values into the formula: \[\mathscr{A}=\frac{1}{2} \times 2 \times 1 = 1.\] Show more…

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Find the area of each triangle using the formula $\mathscr{A}=\frac{1}{2} b h,$ and then verify that the for. mula $\mathscr{A}=\frac{1}{2} a b \sin C$ gives the same result. (Angle can't copy)

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Key Concepts

Triangle Area Calculation

This key concept involves determining the area of a triangle. The most fundamental formula used is A = 1/2 × base × height, where the base of the triangle is any one of its sides and the height is the perpendicular distance from this base to the opposite vertex. This method is applicable in cases where the perpendicular height is known or can be easily computed.

Trigonometric Area Formula

This concept describes an alternative method to calculate the area of a triangle using two sides and the sine of the included angle. The formula A = 1/2 × a × b × sin C is particularly useful when the height is not directly accessible. It exploits the relationship between the lengths of the sides, the measure of the included angle, and the altitude drawn from the vertex opposite the base, demonstrating the interconnectedness of trigonometry and geometry.

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