The length of the side QR of a triangle PQR is 14.5cm <PQR=71 <QRP=57,find the length of the side s PR and PQ

To find the lengths of sides PR and PQ in triangle PQR, we will use the law of sines. The law of sines states that in any triangle, the ratio of the length of a side to the sine of its opposite angle is constant.

Let's start by using the law of sines to find the length of side PR.

1. Identify the known values:
- Length of side QR: 14.5 cm
- Angle PQR: 71 degrees
- Angle QRP: 57 degrees

2. Determine the unknown value:
- Length of side PR (let's call it x)

3. Apply the law of sines:
In triangle PQR, we have:
sin(PQR) / PR = sin(QRP) / QR

Plugging in the known values, we get:
sin(71) / x = sin(57) / 14.5

4. Solve for x:
Cross-multiply to get:
sin(71) * 14.5 = sin(57) * x

Rearrange the equation to solve for x:
x = (sin(71) * 14.5) / sin(57)

Using a scientific calculator, evaluate the right side of the equation to find the value of x.

Now, let's find the length of side PQ.

1. Use the same law of sines equation, but solve for PQ this time:
sin(PQR) / PQ = sin(QPR) / QR

2. Plug in the known values:
sin(71) / PQ = sin(57) / 14.5

3. Solve for PQ:
Cross-multiply to get:
sin(71) * 14.5 = sin(57) * PQ

Rearrange the equation to solve for PQ:
PQ = (sin(71) * 14.5) / sin(57)

Use a scientific calculator to evaluate the right side of the equation to find the value of PQ.

By following these steps, you can find the lengths of sides PR and PQ in triangle PQR.

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Trapezoids $EFGH$ and $QRST$ are congruen

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