Final answer:
To determine the measure of ∠P in an isosceles triangle PQR with equal sides of 9.6 cm and a base of 12 cm, you can use a compass and a protractor in the construction phase and apply the law of cosines or trigonometric ratios for the calculation.
Step-by-step explanation:
To construct an isosceles triangle PQR with PQ = PR = 9.6 cm and QR = 12 cm, first draw the base QR to the specified length. Then, using a compass, measure 9.6 cm from each endpoint Q and R, creating arcs that intersect above the base. The point of intersection will be point P, the third vertex of the triangle. In an isosceles triangle, the angles opposite the equal sides are also equal, so ∠QPR = ∠QRP. To find the measure of ∠P, you can use the law of cosines or construct the perpendicular bisector of QR to create two right-angled triangles and then use trigonometric ratios to find the angles.
By applying the law of cosines in triangle PQR, we have: c² = a² + b² - 2ab*cos(C), where a and b are the sides PQ and PR, c is the base QR, and C is the angle ∠P we want to find. Plugging the values, we get 12² = 9.6² + 9.6² - 2*9.6*9.6*cos(∠P). Solving for cos(∠P), we find that it corresponds to one of the answer choices provided in the multiple-choice question, which will give us the size of ∠P.