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Brums [2.3K]
2 years ago
9

In which triangle is the measure of the unknown angle, x, equal to the value of sin–1(StartFraction 5 Over 8. 3 EndFraction)?.

Mathematics
1 answer:
almond37 [142]2 years ago
6 0

The triangle is a right-angled triangle with a perpendicular side of 5 and a hypotenuse of 8.3.

<h2 /><h2>Given to us</h2>

\theta = sin^{-1}\dfrac{5}{8.3}

<h2>Sine θ</h2>

as we know that sine for any angle is the ratio of its perpendicular to the hypotenuse,  and trigonometry is only applicable to a right-angled triangle.

therefore,

\theta = sin^{-1}\dfrac{5}{8.3}\\\\sin \theta=\dfrac{5}{8.3}=\dfrac{Perpendicular}{Hypotenuse}\\

Hence, the triangle is a right-angled triangle with a perpendicular side of 5 and a hypotenuse of 8.3.

Learn more about Sine:

brainly.com/question/18055768

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Expand - 10 (b-9) <br>Please do this quickly ​
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-10b + 90

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3 years ago
#5 Antonio and Abby had the same nimber of paperclips. After Antonio gave 30 paperclips to Abby, Abby had twice as many papercli
Kay [80]

Answer:

#5: 180 paperclips in total.

#6: 126 stamps in total.

#7: Elena should give Lucy 15 colored pencils.

Step-by-step explanation:

This explanation solves each question by setting a single unknown, x.

<h3>#5</h3>

Let x the initial number of paperclips of Antonio. That should also be the number of Abby's paperclips.

Initially:

  • Antonio: x paperclips;
  • Abby: x paperclips.

Antonio gives 30 paperclips to Abby. After that,

  • Antonio: (x - 30) paperclips;
  • Abby: x + 30 paperclips.

Abby now possess twice as many paperclips as Antonio does. In other words,

2(x - 30) = x + 30.

By the distributive property:

2x - 60 = x + 30.

Substract x - 60 from both sides

x = 30 - (-60) = 90.

Both Antonio and Abby initially possess 90 paperclips. That's 180 in total.

<h3>#6</h3>

Similarly, let x be the number of Emily's stamps. That should be the same as the number of Jasmine's stamps.

Initially:

  • Emily: x stamps;
  • Jasmine: x stamps.

After Emily gives 42 stamps to Jasmine:

  • Emily: x-42 stamps;
  • Jasmine: x+42 stamps.

Jasmine now possesses twice as many stamps as Emily does. In other words,

2(x-42) = x+42.

x = 42 + 2\times 42 = 126.

Jasmine used to possess 126 stamps. Now she possesses 126 + 42 = 168 stamps after receiving 42 stamps from Emily.

<h3>#7</h3>

Let the number of pencils that Elena needs to give to Lucy be x.

Initially:

  • Elena: 60 pencils;
  • Lucy: 26 pencils.

After Elena gives x pencils to Lucy:

  • Elena: 60 - x pencils;
  • Lucy: 26 + x pencils.

Elena should now possess four more pencils than Lucy does. In other words,

\underbrace{60 - x}_{\text{Elena's}} = \underbrace{(26 + x)}_{\text{Lucy's}} +4.

2x = 30.

x = 15.

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