Mathematics: PQR is a triangle. PR= 23cm, PQ= 22cm and angle QPR= 48 degrees. Calculate length of QR.

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PQR is a triangle. PR= 23cm, PQ= 22cm and angle - id232213774996, cyndalulu3637

datstepparoddoe27

17.07.2021

The length of QR is approximately 18.3 cm

Step-by-step explanation:

The given parameters are;

The length of the side PR = 23 cm

The length of the side PQ = 22 cm

The measure of the angle QPR = 48°

By cosine rule, we have;

$\overline{QR}^2 = \overline{PR}^2 + \overline{PQ}^2 - 2 \times \overline{PR} \times \overline{PQ} \times cos(\angle QPR)$

Plugging in the values gives;

$\overline{QR}^2 = 23^2 + 22^2 - 2 \times 23 \times 22\times cos(48^{\circ}) \approx 335.84$

$\therefore \overline{QR} \approx \sqrt{335.84} \approx 18.3$

The length of QR ≈ 18.3 cm

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