A tree is broken by wind forms a right angled triangle with the ground. If the broken part makes an angle 60 degree with the ground and the top of the tree is now 20 metre from its base,how tall was the tree?
Tan60 = h1/d = h1/20. h1 = ?.
Cos60 = d/h2 = 20/h2. h2 = ?.
h = h1 + h2 = Ht. of tree.
To find the height of the tree, you can use trigonometry and the concept of similar right-angled triangles. Here's how to solve the problem step by step:
Step 1: Draw a diagram with the given information. The diagram should show the tree, the broken part, the angle of 60 degrees, and the 20-meter distance from the top of the tree to its base.
Step 2: Identify the right-angled triangle formed by the broken part of the tree and the ground. Label the top of the tree as point A, the base as point B, and the point where the tree broke as point C.
Step 3: Use the trigonometric function tangent (tan) to find the height of the tree. The tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the tree (AB), and the adjacent side is the 20-meter distance from the top of the tree to its base (BC).
So, tan(60 degrees) = AB / BC.
Step 4: Calculate the value of tan(60 degrees). The tangent of 60 degrees is √3 (approximately 1.732).
So, √3 = AB / 20.
Step 5: Rearrange the equation to solve for AB (the height of the tree). Multiply both sides of the equation by 20.
AB = √3 * 20.
Step 6: Calculate the value of AB.
AB = 1.732 * 20 = 34.64 meters.
Therefore, the height of the tree is approximately 34.64 meters.