One angle of an isosceles triangle is 150 degrees. ifthe
area of the triangle is 9 square feet, what is the perimeter ofthe
triangle?

Perimeter would be 23.57 ft ( approx)

Step-by-step explanation:

Consider triangle ABC is an isosceles triangle,

In which AB = AC,

And, m∠A = 150°,

∵ AB = AC ⇒ m∠B = m∠C,

Now sum of all interior angles of a triangle is 180°,

i.e. m∠A + m∠B + m∠C = 180°,

150°+ m∠B + m∠B= 180°,

2m∠B + 150° = 180°

2m∠B = 30°

⇒ m∠B = 15°

Let D ∈ BC such that AD ⊥ BC,

∵ Altitude of an isosceles triangle is its median,

i.e, BD = DC or BD = BC

In triangle ADB,

tan 15° =

             .............(1)

Now, area of triangle ABC =

If area = 9 square ft,

From equation (1),

From equation (1),

Using Pythagoras theorem,

Hence, perimeter of the triangle ABC= AB + BC + CA

= 5.99 + 11.59 + 5.99

= 23.57 ft

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.