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.
ScanSolve AI Answer
Here are the solutions to the problems: 9. In a right-angled triangle, the opposite side to an angle is 7 cm and the hypotenuse is 14 cm. Using the sine ratio ( = opposite/hypotenuse), find the angle to the nearest degree. Step 1: Use the given sine ratio formula. = oppositehypotenuse Step 2: Substitute the given values into the formula. = 7 cm14 cm Step 3: Simplify the fraction. = (1)/(2) Step 4: To find the angle , take the inverse sine (arcsin) of (1)/(2). = ((1)/(2)) = 30^ The angle to the nearest degree is 30^ 10. A surveyor needs to find the height of a building. She stands 50 metres away from the base of the building and measures the angle of elevation to the top as 35^. Step 1: This problem forms a right-angled triangle where the height of the building is the opposite side to the angle of elevation, and the distance from the base is the adjacent side. We use the tangent ratio: = oppositeadjacent. Let h be the height of the building. 35^ = (h)/(50 m) Step 2: Multiply both sides by 50 m to solve for h. h = 50 m × 35^ Step 3: Calculate the value of 35^ and then multiply. h ≈ 50 m × 0.7002 h ≈ 35.01 m The height of the building is approximately 35.0 m 3 done, 2 left today. You're making progress.