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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You're on a roll — 5. From the top of a 20 m high cliff the angle of a depression of a b information on a diagram. Since the question is cut off, we will draw a diagram showing a 20 m high cliff and a generic angle of depression. Step 1: Draw a vertical line representing the cliff and a horizontal line from its top. Step 2: Draw a line of sight from the top of the cliff downwards to an object. Step 3: Label the height of the cliff as 20 m and the angle between the horizontal line of sight and the downward line of sight as the angle of depression, . % Cliff [thick] (0,0) -- (0,2); [left] at (0,1) 20 m; [below] at (0,0) Ground; % Observer at top of cliff [above left] at (0,2) Observer; % Horizontal line of sight [dashed] (0,2) -- (3,2); [above] at (1.5,2) Horizontal Line of Sight; % Object (boat) [below] at (3,0) B; [thick] (0,0) -- (3,0); % Ground line % Line of sight to object [thick] (0,2) -- (3,0); % Angle of depression pic [draw, angle radius=0.7cm, ""] angle = (3,2) -- (0,2) -- (3,0); 6. What is the back bearing of 200°? Step 1: Determine if the given bearing is greater than or equal to 180^. The given bearing is 200^. Since 200^ 180^, we subtract 180^ to find the back bearing. Step 2: Calculate the back bearing. Back Bearing = 200^ - 180^ = 20^ Step 3: Express the back bearing in three digits. The back bearing is 020^. 7. A ship sails NW from a port to take supplies to an oil rig. What is the bearing to return from the oil rig to the port? Step 1: Determine the bearing from the port to the oil rig. Sailing NW (North-West) means the direction is 45^ west of North. Measured clockwise from North, this is 360^ - 45^ = 315^. So, the bearing from the port to the oil rig is 315^. Step 2: Calculate the back bearing from the oil rig to the port. Since the bearing from the port to the oil rig (315^) is greater than 180^, we subtract 180^ to find the back bearing. Back Bearing = 315^ - 180^ = 135^ The bearing to return from the oil rig to the port is 135^. 8. Ben and Emma are out flying a kite. Emma can is making a 70° angle with the ground. The kite 50 feet away. To the nearest foot, how many f Assuming "50 feet away" refers to the length of the kite string (the hypotenuse of the right-angled triangle formed by the kite, the ground, and the string), and the question asks for the height of the kite. Step 1: Identify the known values and the unknown. • Angle of elevation () = 70^ • Length of kite string (hypotenuse) = 50 feet • Height of the kite (opposite side) = h Step 2: Choose the appropriate trigonometric ratio. Since we know the hypotenuse and the angle, and we want to find the opposite side, we use the sine function: () = oppositehypotenuse Step 3: Substitute the known values into the formula. (70^) = (h)/(50) Step 4: Solve for h. h = 50 × (70^) Step 5: Calculate the value and round to the nearest foot. Using a calculator, (70^) ≈ 0.93969. h ≈ 50 × 0.93969 h ≈ 46.9845 Rounding to the nearest foot: h ≈ 47 feet The height of the kite is approximately 47 feet. Send me the next one 📸