Triangle with One Obtuse Angle

Introduction for obtuse angle:

Let us discuss about one obtuse angle triangle.

The measurement of angle between 90° and less 180° is called as an obtuse angle. The angles 95°, 100°, 130°, 162° and 178° are some examples of obtuse angles.

From the law of cosines, it can be given as,

Cos C = a^2+b2-c2/2ab

For an angle to be obtuse, C < 0. Therefore, an obtuse angle which satisfies one of the following a^2+b2
I am planning to write more post on free math homework help, how to solve linear inequalities. Keep checking my blog.

Surface Area Equation for One Obtuse Angled Triangle:

The triangle with one obtuse angle which can be given as,

A = bh/2 = b/2 √ [a^2-{(c2+a^2+b2)/2b}2

If S = 1/2 (a+b+c),then

A = √ [s(S-a)(S-b)(S-c)].

Problems for Triangle with One Obtuse Angle:
Example1:

In triangle with one obtuse angle, a right angled triangle has one other angle that is 45º. What is the measurement of the third angle?

Solution:

In the triangle with one obtuse angle, A right triangle angle = 90°. Sum of the angles which are known and to be added 90° + 45º = 135°.

The sum of all the angles in a given triangle is 180º. Subtract the sum of known angles from 180°.                    180° – 135° = 45°

The size of the third angle is 45°.

Example2:

Whether it is possible for a triangle in which it consists of an obtuse angle or more?

Solution:

Let the angles of the triangle be f,g and h . Let f be the obtuse angle.

The sum of all the angles in any triangle is 180º. f + g + h = 180º.

If f > 90º then g + h must be less than 90º. Therefore, g and h must be acute angles.

So therefore no triangle with one obtuse angle is present.

Example3:

In triangle with one obtuse angle,if an Obtuse angled triangle has sides 2 units, 4 units and X units. Then how many such triangles exist?

Solution:

For the triangle with one obtuse angle which can be given as follows,

If x^2+2^2=4^2, this implies that its a right angled triangle. Therefore for the triangle to be Obtuse angled triangle, x^2+ 2^2<4 8.="8." a="a" be="be" br="br" can="can" condition="condition" fulfill="fulfill" if="if" less="less" of="of" ow="ow" satisfied="satisfied" sides="sides" sum="sum" than="than" the="the" this="this" to="to" total="total" triangle="triangle" would="would" x="x">
If 2^2 + 4^2 = x^2

x = 4, it is a right angled triangle.

So, x > 4.So, 4