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Anestetic [448]
3 years ago
11

The length of which line segment is equal to the exact value of the sine if theta?

Mathematics
1 answer:
Ainat [17]3 years ago
4 0
<h3>Answer: Option 2. Segment TS</h3>

====================================================

Explanation:

Recall that the sine of an angle is equal to the ratio of opposite over hypotenuse.

In other words,

sin(angle) = opposite/hypotenuse

With respect to reference angle theta, the side TS is opposite this angle. It is the leg furthest from the angle. The hypotenuse is the longest side segment TO. The hypotenuse is always opposite the 90 degree angle.

For a unit circle, the radius is 1, so segment TO is 1 unit long.

Therefore,

sin(angle) = opposite/hypotenuse

sin(theta) = TS/TO

sin(theta) = TS/1

sin(theta) = TS

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Please help
Alekssandra [29.7K]

Answer:

25 in x 15 in

Step-by-step explanation:

Given:

  • Length = 3/5 the width
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Let width = x

Therefore, length = 3/5 x

First create an equation for the area of the picture based on the given information for its width and length:

\begin{aligned} \implies \textsf{Area of original picture} & = \sf width \times length\\& = x\left(\dfrac{3}{5}x\right)\\& = \dfrac{3}{5}x^2\end{aligned}

We are told the area of the enlarged picture is 375 in².  Therefore, substitute this into the equation and solve for x to find the width of the enlarged picture:

\begin{aligned}\textsf{Area} & = 375\\ \implies \dfrac{3}{5}x^2 & = 375\\ x^2 & =375 \cdot \dfrac{5}{3}\\ x^2 & =625\\ x & = \sqrt{625}\\ x& = 25\end{aligned}

Therefore, the width of the enlarged picture is 25 in.

Substitute the found value of x into the expression for length to find the length of the enlarged picture:

\begin{aligned}\sf Length & = \dfrac{3}{5}x\\\\\implies \sf Length & = \dfrac{3}{5}(25)\\\\& = 15\: \sf in\end{aligned}

Therefore, the dimensions of the enlarged picture are <u>25 in x 15 in</u>.  The width is 25 in and the length is 15 in, as the length is 3/5 of the width.

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2 years ago
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There are many combinations you can use to get to $6. However, I'm not sure what the format is. For example, you could buy 4 twizzler packs and then use the remaining money to find out how many M&Ms you bought. But this seems to be open to answers. Sorry
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