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
Step 1: Identify the components of the right-angled triangle formed. Let h be the height of the standing part of the tree and L be the length of the broken part that touches the ground. The total height of the tree is H = h + L. The distance from the foot of the tree to where the top touches the ground is 8 m. The angle made by the broken part with the ground is 30^. Step 2: Calculate the height of the standing part of the tree (h). We use the tangent function, which relates the opposite side (h) to the adjacent side (8 m). () = oppositeadjacent (30^) = (h)/(8) We know that (30^) = (1)/(sqrt(3)). (1)/(sqrt(3)) = (h)/(8) h = (8)/(sqrt(3)) m Step 3: Calculate the length of the broken part of the tree (L). We use the cosine function, which relates the adjacent side (8 m) to the hypotenuse (L). () = adjacenthypotenuse (30^) = (8)/(L) We know that (30^) = sqrt(3)2. sqrt(3)2 = (8)/(L) L = (8 × 2)/(sqrt(3)) L = (16)/(sqrt(3)) m Step 4: Calculate the total height of the tree (H). The total height is the sum of the standing part and the broken part. H = h + L H = (8)/(sqrt(3)) + (16)/(sqrt(3)) H = (8 + 16)/(sqrt(3)) H = (24)/(sqrt(3)) To rationalize the denominator, multiply the numerator and denominator by sqrt(3): H = (24)/(sqrt(3)) × sqrt(3)sqrt(3) H = 24sqrt(3)3 H = 8sqrt(3) m The height of the tree is 8sqrt(3) m. Send me the next one 📸