1. Find All Three Angles

Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his gardenwill be 55 square yards, find, to the nearest tenth of a degree, the three angles of the triangle.

My Work:

I had no idea how to solve this question. I know that it involves geometry. An isosceles triangle has two equal sides and one side that is different. I also know that the base angles of an isosceles triangles are equal. The formula to find the area of a triangle is A = (1/2)(bh).

I plugged 55 for area and got this equation:

55 = (1/2)(bh) but was not able to go forward because I don't know the base and height of this triangle.

What is the correct method for solving this question?

2. Originally Posted by magentarita
Gregory wants to build a garden in the shape of an isosceles triangle with one of the congruent sides equal to 12 yards. If the area of his gardenwill be 55 square yards, find, to the nearest tenth of a degree, the three angles of the triangle.

My Work:

I had no idea how to solve this question. I know that it involves geometry. An isosceles triangle has two equal sides and one side that is different. I also know that the base angles of an isosceles triangles are equal. The formula to find the area of a triangle is A = (1/2)(bh).

I plugged 55 for area and got this equation:

55 = (1/2)(bh) but was not able to go forward because I don't know the base and height of this triangle.

What is the correct method for solving this question?
Have you learned that area $= \frac{1}{2} a b \sin C$?

Then $55 = \frac{1}{2} (12)(12) \sin C \Rightarrow \sin C = \frac{55}{72} \Rightarrow C = \, ....$

Note now that since the triangle is isosceles, the other two angles are equal ....

3. I see...

Originally Posted by mr fantastic
Have you learned that area $= \frac{1}{2} a b \sin C$?

Then $55 = \frac{1}{2} (12)(12) \sin C \Rightarrow \sin C = \frac{55}{72} \Rightarrow C = \, ....$

Note now that since the triangle is isosceles, the other two angles are equal ....
I had no idea that I needed to use trigonometry to find the 3 angles.

4. Originally Posted by magentarita
I had no idea that I needed to use trigonometry to find the 3 angles.
When you have a triangle and you're given stuff about sides and area and you're asked stuff about angles, trigonometry should be the very first thing that pops into your cranium. Triangles and trigonometry go together like beer and piza.

5. ok....

Originally Posted by mr fantastic
When you have a triangle and you're given stuff about sides and area and you're asked stuff about angles, trigonometry should be the very first thing that pops into your cranium. Triangles and trigonometry go together like beer and piza.
I'll have to memorize that one, too.