### Math Notes

Subjects

#### Trigonometry Solutions

##### Topics || Problems

The area of a rectangular pentagon is 560 square ft. Find the radii of the circumscribed and inscribed circles.

The area of the regular pentagon can be calculated throught the formula $$A_p =5 \frac{1}{2} b~r_i$$ and $$A_p = 5 \frac{1}{2} \sin 72^o r_{c}^{2}$$

$$560 = 5\frac{1}{2} \sin 72^o r_c^2$$

$$r_c = \sqrt{\frac{560x2}{5\sin 72^o}}$$

$$r_c = 15.35~ft$$

Solve the value of $$b$$

$$\cos 54 = \frac{\frac{b}{2}}{r_c}$$

$$b = 2(15.35)(\cos 54)$$

$$b = 18.041 ~ft$$

Solve $$r_i$$

$$560 = 5 \frac{1}{2} (18.041)r_i$$

$$r_i = \frac{560x2}{5x18.041 }$$

$$r_i = 12.42~ft$$