If a tree casts a shadow of 10 meters and the angle of elevation to the top of t

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Question: If a tree casts a shadow of 10 meters and the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

Options:

Correct Answer: 10

Solution:

height = shadow * tan(45°) = 10 * 1 = 10 meters

If a tree casts a shadow of 10 meters and the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

If a tree casts a shadow of 10 meters and the angle of elevation to the top of the tree is 45 degrees, what is the height of the tree?

Step 1: Understand that the tree, the ground, and the shadow form a right triangle.
Step 2: Identify the parts of the triangle: the height of the tree is one side, the shadow is the other side, and the angle of elevation is the angle between the ground and the line from the top of the tree to the end of the shadow.
Step 3: Note that the angle of elevation to the top of the tree is 45 degrees.
Step 4: Recall that the tangent of an angle in a right triangle is the ratio of the opposite side (height of the tree) to the adjacent side (length of the shadow).
Step 5: Write the formula: tan(angle) = height / shadow.
Step 6: Substitute the known values into the formula: tan(45°) = height / 10 meters.
Step 7: Know that tan(45°) equals 1, so the equation becomes: 1 = height / 10 meters.
Step 8: Solve for the height by multiplying both sides by 10 meters: height = 10 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the tree to the length of its shadow and the angle of elevation.
Angle of Elevation – Understanding that the angle of elevation is measured from the horizontal line up to the top of the tree.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the tree is the opposite side, the shadow is the adjacent side, and the angle of elevation is given.