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Find the missing side. Round to the nearest tenth. y=?

Find the missing side. Round to the nearest tenth. y=?-example-1
User Shanda
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I believe it’s 140 I rounded it and got 140 so it should work
User Nannette
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The length of side
\( y \) is approximately
\( 103.1 \) when rounded to the nearest tenth.

To find the missing side y of the right-angled triangle, we can use the trigonometric functions. Given the angle of
\( 43^\circ \) and the opposite side x, we can use the tangent function to find side y. The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.

Here's the step-wise method:

1. Set up the equation using the tangent function:


\[ \tan(43^\circ) = (x)/(y) \]

2. Since we know the length of the hypotenuse (141), we can use the sine function to find x, and then solve for y using the tangent function. For the sine function:


\[ \sin(43^\circ) = (x)/(141) \]

3. Solve for x:


\[ x = 141 * \sin(43^\circ) \]

4. Once x is found, rearrange the tangent function to solve for y:


\[ y = (x)/(\tan(43^\circ)) \]

5. Plug in the value of x into the equation to find y.

Let's perform the calculations.

To find the missing side y of the right triangle, here are the steps and the calculated values:

1. We set up the equation using the tangent function for angle
\( 43^\circ \) and side x:


\[ \tan(43^\circ) = (x)/(y) \]

2. We use the sine function to find the length of side x (the side opposite to the
\( 43^\circ \) angle):


\[ \sin(43^\circ) = (x)/(141) \]

3. We calculate the length of side x:


\[ x = 141 * \sin(43^\circ) \]


\[ x \approx 96.2 \]

4. We rearrange the tangent function to solve for y:


\[ y = (x)/(\tan(43^\circ)) \]

5. We plug in the value of
\( x \) into the equation to find y:


\[ y \approx (96.2)/(\tan(43^\circ)) \]


\[ y \approx 103.1 \]

Hence, the answer is approximately
\( 103.1 \).

User Ichorville
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8.2k points

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