The lenght of each of the two sides of an isisceles triangle is 10 meters. The angle between the two congruent sides is x. find the area of the triangle as a function of x/2.
area = 1/2 base * height
= 1/2 * 2(10sin(x/2)) * 10cos(x/2)
= 100 sin(x/2)cos(x/2)
= 50 sin(x)
To find the area of an isosceles triangle, we can use the formula A = (1/2) * b * h, where A is the area, b is the base, and h is the height.
In this case, the length of each of the two congruent sides of the triangle is given as 10 meters. Let's call the base of the triangle b and the height h.
Since the triangle is isosceles, the base (b) is the same as one of the sides. Therefore, b = 10 meters.
To find the height (h) of the triangle, we need to use trigonometry. The height divides the triangle into two right-angled triangles, each having an acute angle of x/2.
Using trigonometry, we can determine the relationship between the height and the side length, as follows:
sin(x/2) = (h / 10)
To isolate h, we can rearrange the equation as follows:
h = 10 * sin(x/2)
Now that we know the base (b) and the height (h) of the triangle, we can calculate the area using the formula:
A = (1/2) * b * h
Substituting the values we have:
A = (1/2) * 10 * 10 * sin(x/2)
Simplifying further:
A = 5 * 10 * sin(x/2)
Therefore, the area of the isosceles triangle can be expressed as a function of x/2 as:
A = 50 * sin(x/2)