a. Find PR in the diagram b. Find the perimeter of quadrilateral PQRS

Answer:Step-by-step explanation:The quadrilateral has 4 sides and only two of them are equal.A) to find PR, we will consider the triangle, PRQ. Using cosine rulea^2 = b^2 + c^2 - 2abcos AWe are looking for PRPR^2 = 8^2 + 7^2 - 2 ×8 × 7Cos70PR^2 = 64 + 49 - 112 × 0.3420PR^2 = 113 - 38.304 = 74.696PR = √74.696 = 8.64B) to find the perimeter of PQRS, we will consider the triangle, RSP. It is an isosceles triangle. Therefore, two sides and two base angles are equal. To determine the length of SP,We will use the sine rule because only one side,PR is knownFor sine rule,a/sinA = b/sinBSP/ sin 35 = 8.64/sin110Cross multiplying SPsin110 = 8.64sin35SP = 8.64sin35/sin110SP = (8.64 × 0.5736)/0.9397SP = 5.27SR = SP = 5.27The perimeter of the quadrilateral PQRS is the sum of the sides. The perimeter = 8 + 7 + 5.27 + 5.27 = 25.54 cm