Investigating the Relationship Between the Lengths, Perimeter and Area of a Right Angle Triangle

To study the relationship between the length, perimeter and area of ​​a right triangle object To study the relationship between the length, perimeter and area of ​​right triangle. Pythagorean theorem is a 2 + b 2 = c 2. "A" is the shortest side, "b" is the center side, "c" is the longest side of the right triangle. Therefore, the numbers 3, 4, 5 of (minimum number) 2 + (intermediate number) 2 = (maximum number) 2 are 32 = 3 x 3 = 942 = 4 x 4 = 1652 = 5 x 5, + 42 = 52 is satisfied. = 25 Therefore, the numbers 5, 12, 13 and 7, 24, 25 of 32 + 42 = 9 + 16 = 25 = 52 can also be used for this theorem. 52 + 122 =

The generalization of this theorem is the law of cosine, given the length of the other two sides and the angle between them, you can calculate the length of any side of any triangle. If the angle between the opposite side is right angle, the cosine law is reduced to Pythagorean equation. As shown, suppose ABC represents a right triangle and right angle is in C. The height is plotted from point C, and H is called the intersection with AB side. Point H divides the length of the hypotenuse c into parts d and e. The new triangle ACH is similar to the triangle ABC. Both of them are right angles (by height definition), because they share angles with A. In other words, the third angle is the same for both triangles. It is inside. Through similar reasoning, the triangle CBH is also like ABC.

Let ABC be a triangle with sides a, b, c, a2 + b2 = c2. Create a second triangle with side lengths a and b, including right angles. According to the Pythagorean theorem, the hypotenuse of a triangle has a length c = √ a 2 + b 2, which is the same as the hypotenuse of the first triangle. Since the sides of the two triangles are of the same length a, b, c, the triangles are congruent and must have the same angle. Therefore, the angle between the length a of the original triangle and the side of b is right angle.

K11.3. To describe the area formula, use the standard formula A = 1/2 bh of the triangle area. A = 1/2 absin C where a and b are the sides of the triangle and C is a measure of the angle between the triangles. Please use it to find the area of ​​the triangle. K12.1. * Knowing the sine and cosine of a trigonometric function, all trigonometric functions can be extended to a periodic function on a solid line by defining it as a function on a unit circle arc of 0 to 360 degree angle The measured value is the arc from the center. The length of the unit circle corresponding to the angle and likewise the arc length s of the circle with the radius r corresponding to the central measuring angle t radians is s = rt.