Question

1. a triangular garden (shown below) must be enclosed by a fence. how much will it cost to enclose the garden if fencing costs $11.75 per metre? sine law

Explanation:

Step1: Find angle A

The sum of angles in a triangle is 180°. So, $A=180^{\circ}-49^{\circ}-55^{\circ}=76^{\circ}$.

Step2: Use sine - law to find side b

By the sine - law $\frac{a}{\sin A}=\frac{b}{\sin B}$. Substituting $a = 22$ m, $A = 76^{\circ}$, and $B = 49^{\circ}$, we get $b=\frac{22\times\sin49^{\circ}}{\sin76^{\circ}}\approx17.17$ m.

Step3: Use sine - law to find side c

Again, by the sine - law $\frac{a}{\sin A}=\frac{c}{\sin C}$. Substituting $a = 22$ m, $A = 76^{\circ}$, and $C = 55^{\circ}$, we get $c=\frac{22\times\sin55^{\circ}}{\sin76^{\circ}}\approx18.67$ m.

Step4: Calculate the perimeter P

$P=a + b + c=22+17.17+18.67 = 57.84$ m.

Step5: Calculate the cost

The cost of fencing is $11.75\times P$. So, the cost $=11.75\times57.84 = 679.62$.

Answer:

$679.62$