if the vortex angle of an isoceles triangle measures 30 degrees and each of the leg measures 4 the area is?

Answer 1

Area of a triangle = a*b*sin(angle) / 2 {this can be proved by drawing altitude}

angle = angle between a and b {in your problem}

Area = 4*4*sin(30) / 2 = 8*1/2=4

Answer 2

If the vertex angle is 30 degrees than the two base angles must be 75 degrees to add up to a total of 180 degrees. So you have a pair of right triangles with a hypotenuse of 4" and an angle of 75 degrees that you want to find the base of and the height of.

You can find those with the definition of sine and cosine for the 75 degree angle. Then you use the area of a triangle = 1/2 times Base times height to get each triangle's area and double it to get the total area of the original triangle.

The sine of 75 degrees is .9659 and its cosine = .2588. Using sine = opp/hyp then for .9859 times 4 = 3.94 inches tall. Using cosine = adj/hyp then for .2588 times 4= 1.03.

Now total area = 3.94x1.03 = 4 sq inches.

Answer 3

Basis = 2*4 sin 15
Heigh= 4 cos 15

BH/2 = 4* sin 15* 4* cos 15 = 8 * 2sin15 cos15 = 8 sin30o

Since sin 30o = 1/2, then the area is 4

Ana

Answer 4

Ok, just remember, that the area of a triangle can be found like :

Area = a*b*sin(angle) / 2

angle = angle between a and b : so in your problem

Area = 4*4*sin(30) / 2 = 4 u^2

Hope that helps