A ladder 10 meters long leans against a wall, forming a 75° angle with the ground. How high up the wall does the ladder reach? (Round to nearest tenth)
["How High Does a 10-Meter Ladder Reach on a Wall When Leaning at 75°?", "Ever wondered how high a 10-meter ladder reaches when positioned against a wall at a 75° angle to the ground? Understanding the height helps ensure safety and precision in tasks like painting, cleaning, or home repairs. In this article, we’ll break down the trigonometry behind this common scenario to answer: how high up the wall does a 10-meter ladder climb when it makes a 75° angle with the floor?", "---", "### The Right Triangle Setup", "When a ladder leans against a wall, it forms a right triangle:", "- The ladder is the hypotenuse: 10 meters.\n- The angle with the ground is 75°.\n- The height up the wall is the side opposite the angle — what we want to find.", "We use the sine function, defined as:", "> ⬆️ (\sin(\ heta) = \frac{\ ext{opposite}}{\ ext{hypotenuse}})", "Here:", "- (\ heta = 75^\circ)\n- Hypotenuse = 10 m\n- Opposite side = ladder height ((h))", "---", "### Calculating the Height", "Using the sine formula:", "[\n\sin(75^\circ) = \frac{h}{10}\n]", "[\nh = 10 \ imes \sin(75^\circ)\n]", "Using a calculator:", "[\n\sin(75^\circ) \approx 0.9659\n]", "[\nh = 10 \ imes 0.9659 = 9.659 \ ext{ meters}\n]", "---", "### Final Result (Rounded to the Nearest Tenth)", "The ladder reaches approximately 9.7 meters up the wall.", "---", "### Why This Matters", "Knowing the exact height ensures safe positioning — for instance, avoiding overreaching or ensuring ladders meet OSHA safety standards. Whether you're a DIY enthusiast, a handyman, or just curious, understanding basic trigonometry in everyday situations empowers smart decisions.", "---", "### Summary", "- Ladder length (hypotenuse): 10 m\n- Angle with ground: 75°\n- Height achieved: (10 \ imes \sin(75^\circ) \approx 9.659) m\n- Rounded height: 9.7 meters", "---", "Quick fact: For a 75° angle, the ladder reaches just shy of the wall’s top — but never exceeds it, keeping it securely balanced.", "---", "Keywords: ladder height calculation, 10 meter ladder angle, trigonometry ladder, height of ladder against wall, sine formula 75 degrees, home improvement math.", "Use this guide anytime you need to calculate ladder reach safely and accurately!"]
