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4 years ago

8 * 5/7 equalfind the product write the product in its simplest form 8 * 5/7

Mathematics

1 answer:

Naily [24]4 years ago

7 0

The product of 8 and 5/7 is 5.7

Step-by-step explanation:

The given product is $8 \times 5/7$ .

In the product, two terms are given :

The first term 8 is a whole number.
The second term 5/7 is a fraction.

1) So, to find the product of the first term and the second term, one method is to simplify the fraction into decimal number and then perform multiplication operation.

2) Either you can multiply the two terms in the first step and then the division operation is performed at the final step.

First method :

Step 1 : Convert the fraction into decimal

⇒ 5/7 = 0.71

Step 2 : Multiply the result with the other term.

⇒ 8 × 0.71

⇒ 5.68 (approximately 5.7)

Second method :

Step 1 : Multiply both the terms

⇒ 8 ×(5/7) = 40/7

Step 2 : divide 40 by 7

⇒ 40÷ 7 = 5.7

Therefore, the product of 8 and 5/7 is 5.7

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Step-by-step explanation:

In trigonometry, the law of sines is an equation that relates the length of the sides of a triangle (any type of triangle) to the sines of its angles. This is expressed mathematically as

$\displaystyle\frac{a}{\sin \alpha} \ = \ \displaystyle\frac{b}{\sin \beta} \ = \ \displaystyle\frac{c}{\sin \gamma}$ ,

where $a$ , $b$ , and $c$ are the lengths of the sides of the triangle and $\alpha$ , $\beta$ , and $\gamma$ are the opposite angles (as shown in the figure below). Likewise, the law is sometimes written as it reciprocals,

$\displaystyle\frac{\sin \alpha}{a} \ = \ \displaystyle\frac{\sin \beta}{b} \ = \ \displaystyle\frac{\sin \gamma}{c}$ .

Therefore,

$\displaystyle\frac{\sin A}{BC} \ = \ \displaystyle\frac{\sin B}{AC} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sin B \ \times \ BC}{AC} \\ \\ \\\sin A \ = \ \displaystyle\frac{\sin \left(90^{\circ}\right) \ \times \ \sqrt{\left(10\right)^{2} \ - \ \left(\sqrt{78}\right)^{2}}}{10} \\ \\ \\ \sin A \ = \ \dsiplaystyle\frac{\sqrt{22}}{10} \\ \\ \\ \sin A \ = \ 0.47 \ \ \ \ (\text{nearest hundredth})$

Alternatively, you can solve this question using the definition of the trigonometric function sine. For the angle $\theta$ in the figure below,

$\sin \theta \ = \ \displaystyle\frac{\text{opposite}}{\text{hypothenuse}}$ .

Therefore,

$\sin A \ = \ \displaystyle\frac{BC}{AC} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sqrt{\left(10\right)^{2} \ - \ \left(\sqrt{78}\right)^{2}}}{10} \\ \\ \\ \sin A \ = \ \displaystyle\frac{\sqrt{22}}{10} \\ \\ \\ \sin A \ = \ 0.47 \ \ \ \ (\text{nearest hundredth})$