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sweet-ann [11.9K]
3 years ago
14

ILL BRAINLIEST YOU IF YOU PLEASE HELP ME

Mathematics
1 answer:
Harrizon [31]3 years ago
6 0

Answer:

BC ≈ 20.9

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

BC² + AC² = AB²

BC² + 7² = 22²

BC² + 49 = 484 ( subtract 49 from both sides )

BC² = 435 ( take the square root of both sides )

BC = \sqrt{435} ≈ 20.9 ( to the nearest tenth )

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The Johnsons spent a total of ​$69.96 for dinner at their favorite restaurant last night. If this cost included a ​20%​ tip, how
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Find the Value of Sin A rounded to the nearest hundredth, if necessary.
leonid [27]

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})

8 0
3 years ago
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<span><u>Answer </u>
$22,100

<u>Explanation </u>
The first thing you have to find how many weeks are there in one year.
Taking a year to have 365 days and a week to have 7 days, then;
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For 52 weeks = $425.00×52=$22,100 
</span>
6 0
4 years ago
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