This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Hey wild — ready when you are. 2. Write down the bearing of P from A. Step 1: Identify the reference point and direction. The bearing is "from A", so we start at point A. Bearings are measured clockwise from the North line. Step 2: Read the angle from the diagram. The diagram shows an angle of 50^ measured clockwise from the North line at A to the line segment AP. Step 3: Express the bearing in three digits. Bearings are always written with three digits. The bearing of P from A is 050^. 3. Find the exact length of AC. Step 1: Identify the known values in the right-angled triangle. We have a right-angled triangle ABC, with C = 90^. The angle B = 30^. The length of the side adjacent to B is BC = 12. We need to find the length of the side opposite to B, which is AC. Step 2: Choose the appropriate trigonometric ratio. Since we know the adjacent side and want to find the opposite side relative to B, we use the tangent function: () = oppositeadjacent Step 3: Substitute the known values into the formula. (30^) = (AC)/(12) Step 4: Solve for AC. AC = 12 × (30^) Step 5: Substitute the exact value of (30^). The exact value of (30^) is (1)/(sqrt(3)) or sqrt(3)3. AC = 12 × sqrt(3)3 AC = 4sqrt(3) The exact length of AC is 4sqrt(3) units. 4. Q is due East of R and due South of P. The bearing of R from P is 230°. Show this information on the diagram. Since there is no diagram provided for this question, here's how you would construct and label it: Step 1: Draw the points and their relative positions. • Draw point P at the top. • Since Q is due South of P, draw a vertical line segment downwards from P and label the end point Q. This line segment PQ represents the North-South direction. • Since Q is due East of R, draw a horizontal line segment to the left from Q and label the end point R. This line segment RQ represents the East-West direction. • Connect points P and R to form a triangle PQR. The angle at Q ( PQR) will be 90^. Step 2: Mark the bearing of R from P. • At point P, draw a North line pointing vertically upwards. • Measure 230^ clockwise from this North line. Draw a line from P in this direction, which will be the line segment PR. • The angle between the North line at P and the line PR, measured clockwise, is 230^. Step 3: Deduce the angle inside the triangle. • The line PQ points South from P. The angle from the North line to the South line (PQ) is 180^. • The angle from the South line (PQ) to the line PR, measured clockwise, is 230^ - 180^ = 50^. So, QPR = 50^. Drop the next question 📸