Identify the knowns and the unknown in the right-angled triangle.

Here are the solutions for questions 3 and 4. 3. Find the exact length of AC. Step 1: Identify the knowns and the unknown in the right-angled triangle. We are given: • Angle B = 30^. • Side BC = 12 (this is the side adjacent to angle B). We need to find: • Side AC (this is the side opposite to angle B). Step 2: Choose the appropriate trigonometric ratio. Since we have the adjacent side and need the opposite side relative to angle B, we use the tangent function: B = OppositeAdjacent = (AC)/(BC) Step 3: Substitute the known values and the exact value of 30^. We know that 30^ = (1)/(sqrt(3)). 30^ = (AC)/(12) (1)/(sqrt(3)) = (AC)/(12) Step 4: Solve for AC. Multiply both sides by 12: AC = (12)/(sqrt(3)) To rationalize the denominator, multiply the numerator and denominator by sqrt(3): AC = (12)/(sqrt(3)) × sqrt(3)sqrt(3) AC = 12sqrt(3)3 AC = 4sqrt(3) The exact length of AC is 4sqrt(3). 4. Q is due East of R and due South of P. The bearing of R from Q is 270^. Show this information on the diagram. Since no diagram is provided for this question, I will describe how to represent this information. Step 1: Place point Q as a central reference. Step 2: "Q is due East of R" means that if you are at R, Q is directly to your East. Conversely, R is directly to the West of Q. Step 3: "Q is due South of P" means that if you are at P, Q is directly to your South. Conversely, P is directly to the North of Q. Step 4: "The bearing of R from Q is 270^" confirms that R is to the West of Q. From Q, a bearing of 270^ is directly West. To show this on a diagram: • Draw point Q. • Draw a North line from Q. • Draw a line segment extending West from Q, and label the endpoint R. This represents R being due West of Q (or Q being due East of R). • Draw a line segment extending North from Q, and label the endpoint P. This represents P being due North of Q (or Q being due South of P). • Indicate the angle of 270^ clockwise from the North line at Q to the line segment QR. Last free one today — make it count tomorrow, or type /upgrade for unlimited.