Altitude of a Triangle

📌 CONCEPT: The length of the altitude drawn from the vertex of the right angle to the hypotenuse in a right-angled triangle can be calculated using trigonometric ratios, specifically the sine function.

📐 RULE / FORMULA: The formula for finding the length of the altitude (h) is given by h = (a * b) / c, where 'a' and 'b' are the lengths of the two sides containing the right angle and 'c' is the length of the hypotenuse. Alternatively, we can use the formula h = a * sin(θ) if one of the acute angles is known.

💡 WORKED EXAMPLE: Given a right-angled triangle with hypotenuse (c) = 10 cm and one acute angle (θ) = 60°, we can use the sine formula to find the length of the altitude. Since sin(60°) = √3/2, the altitude (h) = 10 * sin(60°) = 10 * (√3/2) = 5√3 cm.

⚠️ COMMON MISTAKE: Students often confuse the formula for the altitude with the formula for the area of a triangle, which can lead to incorrect calculations.