Find the height of the tree if the distance from the observer to the tree trunk is 9 meters

| April 2, 2021 | education

Find the height of the tree if the distance from the observer to the tree trunk is 9 meters, and the area under which he sees the top of the tree is 30 degrees?

Let the height of the tree be the leg of a right-angled triangle AB, the distance from the observer to the trunk of the tree is the leg AC = 9 m, angle C = 30 degrees, angle A = 90 degrees. You need to find AB. Since AB is a leg that lies opposite the angle C, which is 30 degrees, AB is equal to half of the hypotenuse BC: AB = BC / 2. By the Pythagorean theorem, we find the length of BC: BC ^ 2 = AB ^ 2 + AC ^ 2; BC ^ 2 = (BC / 2) ^ 2 + AC ^ 2; BC ^ 2 = BC ^ 2/4 + AC ^ 2; BC ^ 2 = BC ^ 2/4 + 81; BC ^ 2 = (BC ^ 2 + 324) / 4; 4BC ^ 2 = BC ^ 2 + 324 (according to the main property of the “cross to cross” proportion); 4BC ^ 2 – BC ^ 2 = 324; 3BC ^ 2 = 324; BC ^ 2 = 324/3; BC ^ 2 = 108; BC = √108 = 6√3 (m). Find AB: AB = BC / 2 = 6√3 / 2 = 3√3 (m).
Answer: the height of the tree is 3√3 m.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.