# Thread: Forming Functions from Verbal Descriptions

1. ## Forming Functions from Verbal Descriptions

Hey, noob here. I was wondering if any of you smarter guys out there could help me out.
Coming from the textbook "Advanced Mathematics" by Richard Brown...

PROBLEM: Express the area A of a 30*-60*-90* triangle as a function of the length h of the hypotenuse.

TIA

2. Originally Posted by guywhohatesmath
Hey, noob here. I was wondering if any of you smarter guys out there could help me out.
Coming from the textbook "Advanced Mathematics" by Richard Brown...

PROBLEM: Express the area A of a 30*-60*-90* triangle as a function of the length h of the hypotenuse.

TIA
1. Draw the triangle including the height h.

2. The height divide the right angle into 60° and 30° and the hypotenuse c into 2 parts: q under the 60°-angle, p under the 30°-angle.

3. The area of the right triangel is calculated by:

$\displaystyle A=\dfrac12\cdot c \cdot h$

4. $\displaystyle q = h \cdot \tan(60^\circ) = h \cdot \sqrt{3}$

5. $\displaystyle p = h \cdot \tan(30^\circ) = h \cdot \sqrt{\frac13}$

Plug in these values into the equation of the area:

$\displaystyle A= \dfrac12 \left(h \cdot \sqrt{3}+h \cdot \sqrt{\frac13}\right)\cdot h$

After factor out the common factor you'll get:

$\displaystyle A(h)=\dfrac23\sqrt{3}\cdot h^2$

3. Thanks for your time and help. I appreciate it.