A vertical tree stands on one bank of a straight river. From a point A on the opposite bank directly facing the tree, the angle of elevation of the top of the tree is 60^ . A person walks 40 m from A along a straight path on the horizontal ground, making an angle of 30^ with the river bank and moving away from the river. From this new position, the angle of elevation of the top of the tree is 45^ . The width of the r

Step-by-step solution

Let the width of the river be w and the height of the tree be h . From point A , the angle of elevation is 60^ , so h = w 60^ = w 3 . The person walks 40 m from A at an angle of 30^ to the river bank, moving away from the river. The new position B has a component perpendicular to the river bank equal to 40 30^ = 20 m , and a component parallel to the river bank equal to 40 30^ = 20 3 m . The total perpendicular distance from the tree's bank to B is w + 20 . The parallel distance is 20 3 . The square of the horizont