Determining new formulas for all the parameters of the right triangle by knowing t angle bisector and h altitude which belong to the right angle

Right Triangle

Legs of the right triangle: a,b

Hypotenuse: c

Altitude: h

Medians: m_a, m_b, m_c

Angles: α, β

Radius of circumscribed circle: R

Projections of the legs a and b, respectively, onto the hypotenuse c: f, g

Angle bisectors: t_a, t_b, t_c Area: S Perimeter: L

1. Determining the formula of S area for the right triangle by knowing t angle bisector and h altitude which belong to the right angle. The most important formulas to find this form:

This formula is used for determining S area of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

2. Determining the formula of c hypotenuse for the right triangle by knowing t angle bisector and h altitude which belong to the right angle. The most important formulas to find this form:

This formula is used for determining c hypotenuse of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

3. Determining the formula of R radius of circumscribed circle for the right triangle by knowing t angle bisector and h altitude which belong to the right angle.The most important formulas to find this form:

The last formula is used for determining R radius of circumscribed circle of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

4. Determining the formula of a leg for the right triangle by knowing t angle bisector and h altitude which belong to the right angle. The following system is made by using Pythagorean Theorem.

In here, the following formulas in order to determine a leg:

This formula is used for determining a leg of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

5. As the formula is known of the S area for the right triangle, b leg will be determined by using following formulas:

This formula is used for determining b leg of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

6. Determining the formula of r radius of inscribed circle for the right triangle by knowing t angle bisector and h altitude which belong to the right angle. The most important formulas to find this form:

This formula is used for determining r radius of inscribed circle of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

7. Determining the formula of L perimeter for the right triangle by knowing t angle bisector and h altitude which belong to the right angle. The most important formulas to find this form:

This formula is used for determining L perimeter of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

8. Determining the formula of m median for the right triangle by knowing t angle bisector and h altitude which belong to the right angle. The most important formulas to find this form:

The last formula is used for determining m median of circumscribed circle of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

9. Determining the formula of projection of the leg a, respectively, onto the hypotenuse c for the right triangle by knowing t angle bisector and h altitude which belong to the right angle. The most important formulas to find this form:

This formula is used for determining f projection of the leg a respectively, onto the hypotenuse c of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

10. Determining the formula of g projection of the leg b,respectively, onto the hypotenuse c for the right triangle by knowing t angle bisector and h altitude which belong to the right angle. The most important formulas to find this form:

This formula is used for determining g projection of the leg b, respectively, onto the hypotenuse c of the right triangle by knowing t angle bisector and h altitude which belong to the right angle.

References:

1. Alex Svirin “1300 Math Formulas” Copyright © 2004.
2. A. V. Pogorelov “Analytical Geometry” Mir Publishers, Moscow, 1980.
3. Israilov I. I; Pashayev Z. A. “Geometriyadan Masalalar To‘plami” Toshkent, “o‘qituvchi”, 2005.