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A man is placing a ladder against a tree to climb to the top. The ladder is placed 3 feet from the base of the tree.
Bhascara found a right triangle whose area is numerically equal to the length of its hypotenuse. Show that this cannot happen if the triangle has integer sides.
Prove that two Pythagorean triangles with the same area and equal hypotenuses are congruent.
The bottom right hand corner is folded along the crease so that the corner just touches the left hand side of the page.
A 30-foot ladder is leaning up against a roof that is 20 feet above the ground. How far from the building is the foot of the ladder?
The Numbers 3,4, and 5 are called Pythagorean triples since 32 + 42 = 52. The Numbers 5,12, and 13 are also Pythagorean triples since 52 + 122 =132.
Find the length of the diagonal of a rectangular billboard whose sides are 5 feet and 12 feet.
An electron with a mass of 9.11x10-31 kg has a velocity of 4.3 106 in the innermost orbit of a hydrogen atom.
The engine of a sports car rotates at 5,000 revolutions per minute (rpm). Calculate the angular speed of the engine in radians per second.
Use DeMoirvre’s Theorem to find the indicated power of the complex number. Write answer in rectangular form.
The components of v = 240i +300j represent the respective number of gallons of regular and premium gas sold at a gas station.
A pilot in a helicopter sights an ambulance heading toward an accident scene. He measures the angles of depression to the ambulance.
A bicycle tire has a diameter of 20 inches and is revolving at a rate of 10 rpm. At t =0, a certain point is at height 0.
A plane sets a course to fly with a ground speed of 200 km/h due east while climbing at an angle of 14 degrees.
Draw a square on each of the sides of the triangles. Compute the areas of the squares and use this information to investigate.
The line l1 passes through O and through the midpoint of the face ABFE. The line l2 passes through A and through the midpoint of the edge FG.
In the triangle with sides a= 21 cm, b=45cm, and c = 60 cm, where the angle gamma is between the sides a and b.
Use trigonometry to find the height of Building B and the distance between the two buildings. Round your answers to the nearest metre.
A function f:reals->reals is said to be periodic on the reals if there exists a number p greater than zero such that f(x+p)=f(x) for all x in the reals.
Let (x, sin x) be a point on the graph of g near (0,0), and write a formula for the slope of the secant line joining (x, sin x) and (0,0).
If p>3, show that p divides the sum of its quadratic residues that are also least residues.
Find the angle that you would have to shoot it at (assuming the same Vi) in order to hit me between the eyes.
The Pythagorean Theorem can also be proved directly, by choosing 0 at the right angle of a right-angled triangle whose other two vertices are u and v.
The sides of a square are lengthened by 6 cm, the area become 121 cm^2. Find the length of a side of the original square.
An airplane flies 180 kilometers from an airport in a direction of 260 degrees. How far west of the airport is the airplane? How far south?