## Trigonometry (11th Edition) Clone

$1900\text{ square yards}$
The area of the lot is equal to the sum of the areas of the triangle and the sector. First, find the length of the radius of the circle/sector. Note that the radius is actualy the hypotenuse of the right triangle. Hence, ithe radius can be computed using the Pythagorean Theroem to obtain: Let $x$ = radius/hypotenuse Then. \begin{align*} x^2&=30^2+40^2\\ x^2&=900+1600\\ x^2&=2500\\ x&=\sqrt{2500}\\ x&=50\text{ yards} \end{align*} RECALL: (1) The area $A$ of a triangle is given by the formula $A=\frac{1}{2}bh$ where $b=$ base and $h=$ height. (2) The area $A$ of a sector is given by the formula $A=\frac{\theta}{360^o}\pi{r^2}$ where $\theta=$central angle measure in degrees and $r$=radius of the circle. Thus, we have: \begin{align*} \text{Area of the lot} &= \text{Area of the triangle} + \text{Area of the sector}\\ &=\frac{1}{2}(30)(40) + \frac{60^0}{360^o}\pi(50^2)\\\\ &=15(40) + \frac{1}{6}2500\pi\\\\ &=600+1,308.9969389957\\\\ &\approx1900 \text{ square yards} \end{align*}