A wind turbine blade makes a 35° angle with the horizontal. If the blade length is 20 m, find the vertical height from base to tip.
["Title: How to Calculate the Vertical Height of a Wind Turbine Blade at a 35° Angle (with 20m Blade Length)", "---", "Meta Description:\nWant to calculate the vertical height of a wind turbine blade tilted at a 35° angle from the horizontal? Learn the step-by-step trigonometry method using a 20-meter blade length.", "---", "### Introduction", "Wind turbines are marvels of engineering, and understanding their geometry plays a key role in optimizing energy output. One important measurement is the vertical height from the base to the tip of a turbine blade—especially when the blade is angled at 35° from the horizontal. Whether you're studying renewable energy, designing turbine systems, or working in engineering, knowing how to calculate this height using trigonometry is essential.", "In this article, we’ll walk through the math behind finding the vertical height using a 20-meter wind turbine blade angled at 35° above the horizontal.", "---", "### Understanding the Geometry", "A wind turbine blade acts like a slanted beam, forming a right triangle with the horizontal ground:", "- The blade length (20 m) serves as the hypotenuse — the longest side, opposite the angle at the base.\n- The vertical height from the base to the tip is the opposite side relative to the 35° angle.\n- The angle between the blade and the horizontal ground is 35°.", "To find the vertical height, we use the sine function, which relates the opposite side to the hypotenuse:", "[\n\sin(\ heta) = \frac{\ ext{opposite}}{\ ext{hypotenuse}}\n]", "---", "### Step-by-Step Calculation", "1. Write down known values:\n [\n \ heta = 35^\circ, \quad \ ext{hypotenuse} = 20,\ ext{m}\n ]", "2. Use sine to solve for vertical height (h):\n [\n \sin(35^\circ) = \frac{h}{20}\n ]", "3. Rearrange the equation to solve for h:\n [\n h = 20 \ imes \sin(35^\circ)\n ]", "4. Calculate using a calculator:\n [\n \sin(35^\circ) \approx 0.5736\n ]\n [\n h = 20 \ imes 0.5736 = 11.472,\ ext{meters}\n ]", "---", "### Final Result", "The vertical height from the base to the tip of a wind turbine blade that is 20 meters long and angles 35° above the horizontal is approximately:", "> 11.47 meters", "---", "### Why This Calculation Matters", "Knowing the vertical height helps engineers evaluate:", "- Structural loads and balancing forces\n- Aerodynamic efficiency and blade pitch control\n- Tower height requirements and foundation design\n- Optimal energy capture based on rotor geometry", "---", "### Additional Tips", "- Always confirm the angle is measured from the horizontal plane—this ensures correct trigonometric setup.\n- For more precision, use a calculator with sine and tangent functions.\n- This method applies to any blade or structure forming a known angle with a flat base—useful beyond wind energy in civil and mechanical engineering.", "---", "### Conclusion", "Calculating the vertical height of a tilted wind turbine blade is a straightforward but crucial application of trigonometry. For a blade of length 20 meters angled at 35° above the horizontal, the vertical distance from base to tip is roughly 11.47 meters. Mastering this calculation supports better turbine design, safety, and performance in renewable energy systems.", "---", "Keywords: wind turbine blade height, vertical height calculation, trigonometry wind power, 35 degree blade angle, wind turbine geometry, renewable energy engineering, vertical height from base to tip, blade pitch angle, engineering math, solar and wind power angles.", "---", "Need help designing a wind turbine? Explore our guides on turbine blade aerodynamics and optimal angle selection for maximum efficiency."]
