# Geometry problem, area of a triangle

1. Apr 5, 2015

### LogarithmLuke

1. The problem statement, all variables and given/known data
One of the sides of a triangle is 7.0cm, another side is 11.0cm.

A Decide the biggest area this triangle can have.

B Make calculations and show how the triangle could look like if the area is 30 square cm.

2. Relevant equations
Area of a triangle: 0.5*g*h or 0.5*a*b*sinV

3. The attempt at a solution
Well, i tried to think about it but i do not understand fully how to solve the problems. At first i tried to think about the triangle inequality theorem to find out the biggest length the third side could have. I am not desperately looking for answers to the problems, i just want better intuition and understanding so that i can solve similar problems in the future.

2. Apr 5, 2015

### Svein

So what is the maximum of this expression?

3. Apr 5, 2015

### LogarithmLuke

Well, that's what i am struggling with. In my head it has to be 11 times the biggest length the last side can have. I am not too familiar with the sinus values of different angles.

4. Apr 5, 2015

### Svein

From your problem statement: Assume a=7.0cm, b=11.0cm. The all you have to do is finding the maximum of sin(v) for all possible values of v.

5. Apr 5, 2015

### LogarithmLuke

Ah i see now, thanks :) How would you go about solving B?

6. Apr 5, 2015

### certainly

And you should similarly be able to find v for the second question as well. You know v is the angle between a and b.

7. Apr 6, 2015

### epenguin

Equivalently but perhaps more elementary, area = ½ base X height. If you make one side the base, how does the other side have to be disposed to give you maximum height?

Last edited: Apr 6, 2015
8. Apr 6, 2015

### LogarithmLuke

Yeah, you use the b*h when it's a right triangle, if it's not you gotta use trigonometry. I see now that it has to be 90*degrees, but how can we be sure that's the way to solve the problem? How can we know that we don't have to calculate all of the angles using the cosine formula? I mean there are so many ways the triangle could look like.

9. Apr 6, 2015

### vela

Staff Emeritus
Have you drawn sketches? The area is 1/2 x base x height. Pick one side to be the base. How does the height depend on the length of the second side and the angle?