The legs of an isosceles triangle are each 18 cm long and the angle between them measures 48 degrees. What is the length of the third side?
cut the triangle int two identical right triangles by drawing an altitude from the 48 degree corner to the base.
half the length of the third side/18 = sin (48/2)
To find the length of the third side of the isosceles triangle, we need to first determine the type of isosceles triangle and then use trigonometric ratios to solve for the length.
An isosceles triangle has two congruent sides and two congruent angles. In this case, we are given that the two legs are each 18 cm long, and the angle between them measures 48 degrees.
To find the length of the third side, we can use the Law of Cosines, which states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of their lengths and the cosine of the included angle.
In this case, let's denote the length of the third side as 'c'. The two known sides are both 18 cm, and the included angle is 48 degrees. So, we have:
c^2 = 18^2 + 18^2 - 2(18)(18)cos(48)
Now we can solve this equation to find the value of c:
c^2 = 324 + 324 - 648cos(48)
c^2 = 648 - 648cos(48)
c^2 = 648(1 - cos(48))
Using a calculator or trigonometry tables, determine the value of cos(48) and substitute it into the equation to evaluate c^2:
c^2 = 648(1 - 0.6691306)
c^2 = 648(0.3308694)
c^2 ≈ 214.1983912
To find the length of the third side, take the square root of both sides:
c ≈ √214.1983912
c ≈ 14.63 cm
Therefore, the length of the third side of the isosceles triangle is approximately 14.63 cm.