solution of an oblique triangle with two sides equal.

Question

where the included angle is 95 and two sides are 30.

Answer 1

An oblique triangle is any triangle that is not a right triangle.

To solve the triangle ,we need to find two angles and one side.

We assume the given angle is angle A = 95°

The equal sides are b = 30 , c = 30.

Aplly law of Cosines

a² = b²+ c²- 2bc CosA

a²= 30² + 30² -2(30)(30)Cos (95°)

a² = 900 + 900 - 1800 Cos (95°)

a² = 1800  -1800(-0.087)

a² = 1800 + 156.6

a² = 1956.6

a = 44.23

Now we use the The Law of Sines to find the smaller of the other two angles.

Law of Sines SinA/a = SinB/b = SinC/c.

Now we use SinB/b = SinA/a

SinB/30 = Sin(95°)/44.23

SinB/30 = 0.99/44.23

SinB /30 = 0.022

SinB  = 0.022*30

SinB  = 0.66

B  = Sin^-1 (0.66)

B  = 41.29°

Now we find angle C , which is easy using 'angles of a triangle add to 180°.

C   = 180° - (41.29°+ 95°)

C  =  43.71°

 B  = 41.29°, C  = 43.71° and Side a = 44.23.