Understanding Isosceles Triangle and Pythagorean Theorem

Matt uses two 8-foot strings of Christmas lights to form an isosceles triangle. He attaches the lights from stakes to a pole, with the pole's height equal to the distance from the pole to a stake. By applying the Pythagorean theorem, Matt calculates the height of the pole. The equation is solved using square roots, and the final height is approximately 5.66 feet, rounded to the nearest hundredth.

What is the length of each string of Christmas lights used by Matt?

• 10 ft

• 8 ft

• 6 ft

• 12 ft

What shape is formed by the Christmas lights?

• Equilateral triangle

• Right triangle

• Isosceles triangle

• Scalene triangle

Where does Matt attach the strings of lights?

• From the ground to the top of a tree

• From a stake to the top of a pole

• From one stake to another

• From the ground to the roof

What is the relationship between the height of the pole and the distance from the pole to a stake?

• The height is unrelated to the distance

• The height is the same as the distance

• The height is half the distance

• The height is twice the distance

Which theorem is used to determine the height of the pole?

• Cosine rule

• Pythagorean theorem

• Thales' theorem

• Sine rule

What are the lengths of the two legs in the right triangles formed?

• Both are X ft

• One is X ft, the other is 4 ft

• Both are 8 ft

• One is 8 ft, the other is X ft

What is the length of the hypotenuse in the right triangles?

• 16 ft

• 8 ft

• 4 ft

• X ft

What is the simplified form of the equation used to find X?

• X^2 = 16

• 2X^2 = 32

• X^2 = 32

• 2X^2 = 64

What is the approximate height of the pole after solving the equation?

• 4.56 ft

• 5.66 ft

• 7.66 ft

• 6.56 ft

Why do we only consider the positive solution for X?

• Because X is a length

• Because the calculation was incorrect

• Because negative numbers are not allowed

• Because the problem specifies it