a)
The given triangle is an isosceles triangle. A line is drawn to represent the perpendicular height as shown below
AD represents the height of the triangle.
AB = AC = sides of the triangle
Taking angle C as the reference angle,
AC = hypotenuse
CD = 8.5 = adjacent side
AD = opposite side
We would find AC by applying the cosine trigonometric ratio which is expressed as
Cos θ = adjacent side/hypotenuse
Cos36 = 8.5/AC
AC = 8.5/Cos36
AC = 10.51
The length of each side of the triangle is 10.51 m
b) Area of triangle = 1/2 x base x height
To find AB, we would apply Pythagorean theorem which is expressed as
hypotenuse^2 = opposite side^2 + adjacent side^2
10.51^2 = AB^2 + 8.5^2
AB^2 = 10.51^2 - 8.5^2 = 38.21
AB = √38.21 = 6.18
Area = 1/2 x 17 x 6.18
Area of triangle = 52.53 m^2
