dancingmonkey

1. There are 9 dots, and to make triangles, you need 3.

C(9, 3) is 84. However, out of these 84 ways, there are 3 horizontal lines, 3 vertical, and two diagonal (these aren't considered triangles).

Now, we can use complementary counting to find the remaining number of true cases.

84 - (3 + 3 + 2) = 84 - 8 = 76.

Answer: 76 triangles

2. If a right isosceles triangle were to have a hypotenuse of 1, we could find the values of the base and height using the Pythagorean Theorem. 

$x^2 + y^2 = 1^2 = 1$, $x^2 + y^2 = 1$.

Now because the sides are the same length, we can simplify this equation to 

$2x^2 = 1$

$x^2 = \frac{1}{2}$, $x = \sqrt{\frac{1}{2}}$.

To find the area, we use the area equation of a triangle ($\frac{bh}{2}$). Because the base and height are the same, the equation becomes $\frac{b^2}{2}$ or $\frac{h^2}{2}$. 

Plugging the value we got into the equation, we get

$\frac{\sqrt{\frac{1}{2}}^2}{2} = \frac{\frac{1}{2}}{2} = \frac{1}{4}.$

Answer: $\mathbf{\frac{1}{4}}$

Use Law of Cosines for all three problems and you should get the answer pretty quickly.

$\angle A = \frac{5\pi}{6}$

$\angle D = \frac{\pi}{2}$

$\angle G = \frac{\pi}{4}$

hmm...that's weird. do you get that when you enter an equation in the calculator and click the equal sign to solve?

the calculator for web2.0? it works fine for me

I think you kind of have an idea of what this problem is about based on the title of your question. Try using the law of cosines first.