Triangle ABC

Triangle ABC has side lengths m-1, m-2, m-3. What has to be m to be triangle

a) rectangular
b) acute-angled?

Result

m(a) =  6
m(b) =  7

Solution:

(m1)2=(m2)2+(m3)2;m>3 m22m+1=m24m+4+m26m+9 m28m+12=0  m1,2=b±D2a=8±162 m1,2=8±42 m1,2=4±2 m1=6 m2=2  m>3 m(a)=6 (m-1)^2 = (m-2)^2 +(m-3)^2; m>3 \ \\ m^2-2m+1 = m^2-4m+4+m^2-6m+9 \ \\ m^2-8m+12 = 0 \ \\ \ \\ m_{1,2} = \dfrac{ -b \pm \sqrt{ D } }{ 2a } = \dfrac{ 8 \pm \sqrt{ 16 } }{ 2 } \ \\ m_{1,2} = \dfrac{ 8 \pm 4 }{ 2 } \ \\ m_{1,2} = 4 \pm 2 \ \\ m_{1} = 6 \ \\ m_{2} = 2 \ \\ \ \\ m>3 \ \\ m(a) = 6 \ \\

Checkout calculation with our calculator of quadratic equations.

b) m>6b) \ m>6



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:
1st comment
Be the first to comment!
avatar




Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Pythagorean theorem is the base for the right triangle calculator.
Cosine rule uses trigonometric SAS triangle calculator.
See also our trigonometric triangle calculator.

Next similar math problems:

  1. Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  2. If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  3. Medians of isosceles triangle
    iso1 The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians?
  4. The pond
    rybnik_3 We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
  5. Catheti
    pyt_theorem The hypotenuse of a right triangle is 41 and the sum of legs is 49. Calculate the length of its legs.
  6. Angles by cosine law
    357_triangle Calculate the size of the angles of the triangle ABC, if it is given by: a = 3 cm; b = 5 cm; c = 7 cm (use the sine and cosine theorem).
  7. Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  8. Isosceles IV
    iso_triangle In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
  9. RT and circles
    r_triangle Solve right triangle if the radius of inscribed circle is r=9 and radius of circumscribed circle is R=23.
  10. Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  11. Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  12. Theorem prove
    thales_1 We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
  13. Roots
    parabola Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
  14. Equation
    calculator_2 Equation ? has one root x1 = 8. Determine the coefficient b and the second root x2.
  15. Quadratic equation
    kvadrat_2 Find the roots of the quadratic equation: 3x2-4x + (-4) = 0.
  16. Discriminant
    Quadratic_equation_discriminant Determine the discriminant of the equation: ?
  17. Variable
    eq2_12 Find variable P: PP plus P x P plus P = 160