Practice 4b In the diagram, PQRS is a rectangular sloping surface, PQTU is a rectangle on horizontal ground and RI and
SU are vertical lines. PQ = SR=UT = 45 cm, QR = PS = 32 cm and angle RQT= 38º.

Calculate
PR,
(b) RT, and
(c) angle RPT

(a) PR = 55.2 cm

(b) RT = 19.7 cm

(c) <RPT =

Step-by-step explanation:

(a) to determine the value of PR, apply the Pythagoras theorem to PQR.

PQ = 45, and SP = QR = 32. So that;

= +

= +

          = 2025 + 1024

          = 3049

PR =

     = 55.218

PR = 55.2 cm

(b) To determine RT, apply the appropriate trigonometric function to QRT.

Let RT be represented by x, so that;

Sin =

x = 32 * Sin

  = 32 * 0.6157

x = 19.7024

RT = 19.7 cm

(c) To determine <RPT, let the angle be represented by θ.

Sin θ =

        =

Sin θ =

         = 0.3568

θ = 0.35568

  =

Thus, <RPT =