Pythagorean Theorem Problems

Geometry Quiz


The Pythagorean Theorem states that for a right triangle with legs a and b and hypotenuse c,
c2 = a2 + b2

The Cosine Law is a generalization of the Pythagorean Theorem. For a triangle with sides a, b, and c and angle C opposite the side c,
c2 = a2 + b2 − 2ab⋅cos(C)

Question 1: In the figure below, O is the center of circle C and ABO is a right triangle. Calculate the length of the hypotenuse of triangle ABO as a function of the circumference of circle C:

Question 2: Rectangle ABCD in the figure below has AB = 4, AD = 6 and triangle EBC is isosceles, EB = EC. What is the perimeter of triangle EDC?

Question 3: In the figure below, m is the altitude of the equilateral triangle. Calculate the length of a side of the triangle as a function of m.

Question 4: The diagonal AC of rhombus ABCD is 24cm. If the area of the rhombus is 120cm2, calculate the length of side AB in cm.

Question 5: What is the closest approximation of the value of angle a in the figure below, if AB = 7, BC = 11 and CA = 5?

Question 6: The sides a, b, c of a right triangle satisfy the relation a2 + b2 + c2 = 18. What is the value of the hypotenuse c?

Question 7: If AB = a, AC = 2a and ∠BAC = 60°, calculate the sum of squares of the sides of triangle ABC as a function of a.

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