Pythagorean Theorem: Problems with Solutions

Problem 1
Given a right triangle ABC, AB=8 and BC=5, find the square of AC (i.e. AC2 = ?).

Problem 2
Could a right triangle have sides: 3, 4, 5?
Problem 3
Given a right triangle ABC, $$\angle C = 90 ^{\circ}$$, in which AC=3, BC=4. Determine the length of AB.

Problem 4
Given a right triangle ABC, $$\angle C = 90 ^{\circ}$$, in which AC=7, AB=25. Determine the length of BC.

Problem 5
Given a right triangle ABC, $$\angle C = 90 ^{\circ}$$, in which AC=8, BC=15. Determine the length of AB.
Problem 6
A company must stretch a cable from the top of a tower that is 25 meters high to a point 50 meters away from the base of the tower.
Calculate the length of the cable.

Problem 7
Given a square plot of land with distance between two opposite vertexes of $2\sqrt{2}$ kilometers.
Calculate the total area of the plot.

Problem 8
At sunset, a tree projects a shade that is 2.5 meters of length. The distance from the tree top to the most distant end of the shade is 4 meters. What is height of the tree?

Problem 9 sent by Arisha
$$\angle С=90^\circ$$, $$\angle B=30^\circ$$, AB = 6. Find the length of BC.

Problem 10
Calculate the height of the triangle.

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