Question

A triangle ABC, the sides are 6cm, 10cm and 14cm. show that the triangle is obtuse angled with the obtuse angle to 120degree​

Answer 1

Solution:

Let a = 14, b = 10, c = 6

⇒ s = (a + b + c)/2 = 15.

The largest angle is opposite to the largest side.

Hence tan A/2 = √(s - b) (s - c)/s(s - a)

                         = √(5 X 9/15 = √3

⇒ A/2 = 60o ⇒ A = 120o.

Alternative Method: 

cosA = (b2 + c2 - a2)/2bc

          = 100 + 36 - 196/120

          = - 1/2 

⇒ A = 120o.

Hope it helps

Mark it as BRAINLIEST if you are satisfied with the answer

Answer 2

AnswEr :

⋆ Refrence of Image is in the Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(6,8)\linethickness{0.075mm}\put(1, .5){\line(2, 1){3}}\put(4, 2){\line(-2, 1){2}}\put(2, 3){\line(-2, -5){1}}\put(.7, .3){ B }\put(4.05, 1.9){ A }\put(1.7, 2.95){ C }\put(3.2, 2.5){ 10 cm }\put(0.6,1.7){ 6 cm }\put(2.7, 1.05){ 14 cm }\end{picture}$

$\rule{150}{1}$

⋆ Here we Have Sides :

• AB = 14 cm (Longest Side)
• AC = 10 cm
• BC = 6 cm

As, AB is the Longest Side, therefore Angle Opposite to it i.e. ∠ C will be Greater Angle that is Obtuse Angle.

$\rule{200}{2}$

☯⠀$\underline{\textsf{By Using COS Formula for Angle C :}}$

$\dashrightarrow\tt\:\:c^2=a^2+b^2-2ab\cos(c)\\\\\\\dashrightarrow\tt\:\:2ab \cos(c) = a^2 + b^2 - c^2\\\\\\\dashrightarrow\tt\:\: \cos(c) = \dfrac{a^2 + b^2 - c^2}{2ab}\\\\\\\dashrightarrow\tt\:\: \cos(c) = \dfrac{(6)^2 + (10)^2 - (14)^2}{(2 \times 6 \times 10)}\\\\\\\dashrightarrow\tt\:\: \cos(c) = \dfrac{36 + 100 - 196}{120}\\\\\\\dashrightarrow\tt\:\: \cos(c) = \dfrac{ - \:60}{120}\\\\\\\dashrightarrow\tt\:\: \cos(c) = \dfrac{ - \:1}{2} \\\\\\\dashrightarrow\tt\:\:c = \dfrac{1}{ \cos} \times \dfrac{ - \:1}{2}\\\\\\\dashrightarrow\tt\:\:c = \cos^{ -1} \bigg( \dfrac{ -\:1}{2} \bigg)\\\\\\\dashrightarrow\tt\:\:c =\pi -\dfrac{\pi}{3}\\\\\\\dashrightarrow\tt\:\:c = \dfrac{(3\pi - \pi)}{3}\\\\\\\dashrightarrow\tt\:\:c = \dfrac{2\pi}{3}\\\\\\\dashrightarrow\tt\:\:c = \dfrac{2 \times 180}{3}\\\\\\\dashrightarrow\tt\:\:c = (2 \times 60)\\\\\\\dashrightarrow\:\:\underline{\boxed{\red{\tt \angle\:c = 120^{\circ}}}}$

⠀

$\therefore\:\underline{\textsf{It will be Obtused Angled Triangle of \textbf{120 ^{\circ} }.}}$