Using the Pythagorean Theorem: Using variables

Look at the triangles in the figure.

Express the length DB in terms of X.

$\sqrt{32+x^2}$ cm

The triangle in the figure is isosceles.

The length of the hypotenuse is $\frac{x+3}{\sqrt{2}}$ cm.

Work out the length of the leg.

$\frac{x+3}{2}$ cm

Look at the triangle in the figure.

$a+b=7$

The ratio between CB and AC is 5:3.

Calculate: $a,b$.

$a=3\text{ }b=4$

Look at the triangle in the diagram below.

Is it a right triangle?

No, the angle is obtuse.