QuestionFind the height of the tree shown to the right.
Studdy Solution
STEP 1
1. The tree forms a right triangle with the ground and the hypotenuse is the line from the top of the tree to a point on the ground.
2. The hypotenuse of the triangle is 30 feet.
3. The base of the triangle is 17 feet.
4. We need to find the height of the tree, which is the other leg of the triangle.
STEP 2
1. Identify the right triangle components.
2. Apply the Pythagorean theorem.
3. Solve for the height of the tree.
STEP 3
Identify the components of the right triangle: - The hypotenuse is 30 feet. - One leg (base) is 17 feet. - The other leg (height of the tree) is unknown.
STEP 4
Apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:
Substitute the known values into the equation:
STEP 5
Calculate the squares of the known sides:
Substitute these values back into the equation:
STEP 6
Solve for by subtracting 289 from both sides:
STEP 7
Find the height of the tree by taking the square root of :
The height of the tree is:
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