Trigonometry
Objective: Use trigonometry functions to find the area of triangles.

In an isosceles Δ, the two equal sides measure 4 meters, and they include an angle of 40*. Find the area of the isosceles triangle, to the nearest square meter.

Step-by-step explanation:

For a triangle the area is

If our triangle is isosceles and the 2 congruent sides each measure 4 and they include an angle of 40 degrees, let's say that the vertex angle is 40 and the sides that are not the base each measure 4.  If we drop an altitude from the vertex to the base, we cut the triangle into 2 right triangles, with the vertex angle being 20 degrees and the hypotenuse being 4.  To find the base, then, which is opposite the angle, we use the sin ratio:

and

4sin(20) = b so

b = 1.368

But we need the whole base, and that is only half of it.  So

2b = 2.736

To find the height, which is adjacent to the angle, we use the cos ratio:

and

4cos(20) = h so

h = 3.759

Now we have enough info to find the area of the triangle using the triangle area formula from above:

and

A = 5 meters squared.

step-by-step explanation:

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