a)
You are given 3 sides.
The single stroke on each side of the triangle means the two sides are equal.
So the three sides are: 3.8m, 3.8m and 4.8m
To get the angle we use cosine rule:
Cos A = (b² + c² - a²)/(2bc)
Let us solve for the angle facing the 3.8
Cos A = (4.8² + 3.8² - 3.8²) / (23.84.8)
Cos A = (4.8²) / (23.84.8) = 4.8/(23.8) ≈ 0.6316
A = Cos⁻¹(0.6316)
A ≈ 50.8°
Since the triangle is Isosceles triangle, since the side 3.8 are two, so the angles facing it would be same.
50.8° and 50.8°
To solve for the third angle.
Sum of angles in a triangle = 180
50.8 + 50.8 + x = 180
x =180 - 50.8 -50.8
x = 78.4°
So the interior angles in the triangle ≈ 50.8°, 50.8°, 78.4°
b)
Area of triangle: Using Hero's formula, that is when the three sides of the triangle are given.
3.8, 3.8, and 4.8, a = 3.8, b = 3.8, c = 4.8
Hero's formula = √(s(s - a)(s - b)(s - c))
s = (a + b + c)/2
s = (3.8 + 3.8 +4.8)/2 = 12.4/2 = 6.2
Area = √(s(s-a)(s-b)(s-c))
Area = √(6.2 (6.2 - 3.8) (6.2 - 3.8) (6.2 - 4.8))
Area = √(6.2 2.4 2.4 1.4) = √49.9968
Area ≈ 7.07 square meter
For the two triangles ≈27.07 ≈ 14.14 square meter.
Hope this helps.
