in a diagram, PRS is a straight line. PQ = 9.2 cm, QS= 7.6cm and angle QPR =38 degrees.QR is perpendicular to PS.
Calculate angle PQS to nearest 0.1 degrees
by law of sines, 7.6/sin38 = 9.2/sinS
knowing P+S+Q = 180 degrees, now you know Q
all information about R is irrelevant
5.7cm
To calculate angle PQS, we can use the trigonometric relationship in a right triangle. In this case, triangle PQS is a right triangle because QR is perpendicular to PS.
First, we need to find the length of QR. Since QR is perpendicular to PS, triangle PQS and triangle QRS are similar triangles. This means we can use the ratios of corresponding sides to find the length of QR.
Using the given lengths, PQ = 9.2 cm and QS = 7.6 cm, we can set up the proportion:
PQ/QS = QR/SR
Substituting the given values:
9.2/7.6 = QR/SR
To solve for QR, we rearrange the equation:
QR = (9.2/7.6) * SR
Next, we need to find the length of SR. Since PRS is a straight line, SR is the same as PS.
Using Pythagoras' theorem, we have:
PS^2 = PQ^2 + QS^2
Substituting the given values:
PS^2 = 9.2^2 + 7.6^2
PS = √(9.2^2 + 7.6^2) ≈ 11.68 cm
Now that we have the lengths of QR and PS, we can use trigonometry to find the angle PQS.
In triangle PQS, we can use the sine function:
sin(PQS) = QR/PS
Substituting the values obtained:
sin(PQS) = [(9.2/7.6) * SR] / PS
sin(PQS) = [(9.2/7.6) * 11.68] / 11.68
sin(PQS) ≈ 0.9796
To find the angle PQS, we can use the inverse sine function:
PQS = arcsin(0.9796)
PQS ≈ 79.9 degrees (rounded to the nearest 0.1 degrees)
Therefore, angle PQS is approximately 79.9 degrees.