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?

Correct answer:

m(a) =  6
m(b) =  7

Step-by-step explanation:

(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 

Our quadratic equation calculator calculates it.

b) m>6



We will be pleased if You send us any improvements to this math problem. Thank you!



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.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Related math problems and questions:

  • Triangle's centroid
    triangles_1 In the triangle ABC the given lengths of its medians tc = 9, ta = 6. Let T be the intersection of the medians (triangle's centroid) and point is S the center of the side BC. The magnitude of the CTS angle is 60°. Calculate the length of the BC side to 2 d
  • Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  • 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 the AC side into three equal lines. KLM is an isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  • Right angled triangle 2
    vertex_triangle_right LMN is a right-angled triangle with vertices at L(1,3), M(3,5), and N(6,n). Given angle LMN is 90° find n
  • Triangle and its heights
    triangle_2 Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
  • Sides of right angled triangle
    triangle_rt1 One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle.
  • Two groves
    hajovna Two groves A, B are separated by a forest, both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B, if AC = 5004 m, BC = 2600 m and angle ABC = 53° 45 ’?
  • 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).
  • Equilateral triangle ABC
    equliateral In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
  • A rectangle 2
    rectangles A rectangle has a diagonal length of 74cm. Its side lengths are in ratio 5:3. Find its side lengths.
  • Right triangle eq2
    rt_triangle_1 Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
  • Laws
    pyt_triangle From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
  • The right triangle
    rt_triangle_1 In the right triangle ABC with right angle at C we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles.
  • Acute angles
    angles_meter Sizes of acute angles in the right-angled triangle are in the ratio 1: 3. What is size of the larger of them?
  • Medians of isosceles triangle
    iso1 The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What is the length of medians?
  • Triangle ABC
    ABC Right triangle ABC with right angle at the C, |BC|=18, |AB|=33. Calculate the height of the triangle hAB to the side AB.
  • Right triangle - ratio
    rt_triangle The lengths of the legs of the right triangle ABC are in ratio b = 2: 3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle.