From a point on the ground, the angle of elevation to the top of a tree is 45 degrees. If the point is 20 meters away from the base of the tree, what is the height of the tree?
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From a point on the ground, the angle of elevation to the top of a tree is 45 degrees. If the point is 20 meters away from the base of the tree, what is the height of the tree?
Q: From a point on the ground, the angle of elevation to the top of a tree is 45 degrees. If the point is 20 meters away from the base of the tree, what is the height of the tree?
Step 1: Understand the problem. You have a tree and a point on the ground that is 20 meters away from the base of the tree.
Step 2: Know that the angle of elevation to the top of the tree is 45 degrees. This means if you draw a line from the point on the ground to the top of the tree, it makes a 45-degree angle with the ground.
Step 3: Remember that when the angle of elevation is 45 degrees, the height of the tree is equal to the distance from the point to the base of the tree.
Step 4: Use the formula for height: Height = distance * tan(angle). Here, the distance is 20 meters and the angle is 45 degrees.
Step 5: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
Step 6: Substitute the values into the formula: Height = 20 meters * 1.
