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Arlecino [84]
2 years ago
5

The area of triangle ABC is 3√2 square inches. Find the measure of the acute angle, A, if b = 9 meters and c = 2 meters.

Mathematics
1 answer:
taurus [48]2 years ago
3 0

Answer:

A\approx 28^{\circ}

Step-by-step explanation:

Please find the attachment.  

We have been given that area of triangle ABC is 3√2 square inches.

\text{Area}=\frac{1}{2}\text{Base}\times \text{height}

We know that area of triangle an be found using trigonometry as:

\text{Area}=\frac{1}{2}\times c\times h

\text{sin}(A)=\frac{h}{9}\\h=9\cdot \text{sin}(A)

3\sqrt{2}=\frac{1}{2}\times 2\times 9\cdot \text{sin}(A)

3\sqrt{2}=9\cdot \text{sin}(A)

9\cdot \text{sin}(A)=3\sqrt{2}

\text{sin}(A)=\frac{3\sqrt{2}}{9}

\text{sin}(A)=\frac{\sqrt{2}}{3}

Now, we will use inverse sine to find the value of angle A as:

A=\text{sin}^{-1}(\frac{\sqrt{2}}{3})

A=28.1255057^{\circ}

A\approx 28^{\circ}

Therefore, the measure of angle A is approximately 28 degrees.

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Step-by-step explanation:

| 3x + 1 | =22

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Step-by-step explanation:

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Step-by-step explanation:

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The sum of the numbers 8 × 10⁶ and 7.92 × 10⁹ in the form of scientific notation will be 7.928 × 10⁹.

<h3>What is Algebra?</h3>

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression is given below.

8 × 10⁶ and 7.92 × 10⁹

The addition of both terms 8 × 10⁶ and 7.92 × 10⁹ will be

⇒ 8 × 10⁶ + 7.92 × 10⁹

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The sum of the numbers 8 × 10⁶ and 7.92 × 10⁹ in the form of scientific notation will be 7.928 × 10⁹.

More about the Algebra link is given below.

brainly.com/question/953809

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