Question

Match the following
1) In A ABC , b2 = a ² +c
2) In A ABC,
b2 > a2 +c2
3) In A ABC, b2 <a? + c2
a) Obtuse angled triangle
b) Right angled triangle
c) Acute angled triangle​

Answer 1

Answer:

Which angle is obtuse, if in a triangle ABC b^2 + c^2 < a^2?

Angle A is likely to be obtuse

Draw the figure ABC such that the side opposite to side A is a, B is b and C is c

Its given that the side a^2 = b^2 + c^2

Now , we know that any side square in a triangle is equal to the sum of other to side square to which two times subtracted by the multiple of the other to side and cos of the angle

this will become more clear from the example

In the figure you recently draw ,

a^2 = b^2 + c^2 -2bc(cos(A))——————— [eq 1]

a^2 > b^2 + c^2

b^2 + c^2–2bc(cos (A)) > b^2 + c^2

0 > 2bc(cos(A))

Cos(A)<0

From this relation we found that the cos of angle A is greater than 0

We also know that cos 90 is 0 therefore cos A is greater then cos 90

Hence A > 90

Angle that is greater then 90 is considered to be obtuse

HP