From a point on the ground, the angle of elevation to the top of a tree is 45 degrees. If the tree is 10 meters tall, how far is the point from the base 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 tree is 10 meters tall, how far is the point from the base 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 tree is 10 meters tall, how far is the point from the base of the tree?
Step 1: Understand the problem. We have a tree that is 10 meters tall.
Step 2: The angle of elevation from the point on the ground to the top of the tree is 45 degrees.
Step 3: Recall that the tangent of an angle in a right triangle is the opposite side (height of the tree) divided by the adjacent side (distance from the point to the base of the tree).
Step 4: Write the formula for distance: Distance = height / tan(angle).
Step 5: Plug in the values: height = 10 meters and angle = 45 degrees.
Step 6: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
Step 7: Substitute the values into the formula: Distance = 10 meters / 1.
Step 8: Perform the calculation: Distance = 10 meters.
