Applying Pythagorean Theorem and Distance Formula

The diagonal of a rectangle is 27 meters long. If the angle between the diagonal and the long side is 25 degrees, what is the length of the shortest sides?

• 13.4 meters

• 24.5 meters

• 11.4 meters

• 10.7 meters

• AB = 3

  BC = 3

• AB = 6

  BC = 6

I have been given a hypotenuse in this 45-45-90 triangle. How do I find the length of a leg of the triangle?

• Multiply by √2

• Divide by √2

• It's the same length as the hypotenuse.

• Divide by 2

Is a triangle with side lengths 117, 45, and 108 a right triangle?

• yes

• no

A 13 ft. ladder is leaning against the house. The top of the ladder touches the house at 10 feet above the ground. How far away is the bottom of the ladder from the house? (Help me Pythagoras!)

• 10 feet

• 7.5 feet

• 8.3 feet

• 3.8 feet

Find y.

• 11√2

• 11

• 22

• (11√2)/2

The main mast of a fishing boat is supported by a sturdy rope that extends from the top of the mast to the deck. If the mast is 20 feet tall and the rope attached to the deck 10 feet away from the base of the mast, how long is the rope? Round your answer to the nearest thousandth.

• 17.323 ft.

• 22.361 ft.

• 25.241 ft.

• 30.327 ft.

Find the length of variable h.

• 35.60

• 35.00

• 35.71

• 61.03

What is the formula for finding the hypotenuse?

• a²+b²=c²

• a+b=c

• a-b=c

• c-a=c

Study the figure below, which illustrates a dilemma facing the Gainesville City Council. They are going to build a footbridge connecting City Hall to the Municipal Outhouse, because a number of citizens have perished while crossing Big Swamp. The distance from the Court House directly south to City Hall is 1440 feet, and the distance from the Court House directly west to the Municipal Outhouse is 1512 feet. Find the cost of the footbridge, assuming that such a structure costs $21 per foot.

• $43,848

• $54,810

• $61,992

• $65,772