Question

question 9 (1 point) determine the perimeter of this triangle. 63° 14 65.8° 16 less than 46 units more than 46 units exactly 46 units non - existent because the units of measure are not indicated

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a triangle with side lengths $a$, $b$, $c$ is $P=a + b + c$. Here $a = 14$, $b=16$, and we need to find the third - side length $c$.

Step2: Use Law of Cosines

Let the angle opposite to side $c$ be $\theta=180^{\circ}-63^{\circ}-65.8^{\circ}=51.2^{\circ}$. By the Law of Cosines $c^{2}=a^{2}+b^{2}-2ab\cos\theta$. Substitute $a = 14$, $b = 16$, and $\theta = 51.2^{\circ}$ (so $\cos\theta=\cos(51.2^{\circ})\approx0.626$).
$c^{2}=14^{2}+16^{2}-2\times14\times16\times0.626$
$c^{2}=196 + 256-2\times14\times16\times0.626$
$c^{2}=196+256 - 281.856$
$c^{2}=170.144$
$c=\sqrt{170.144}\approx13.04$.

Step3: Calculate perimeter

$P=a + b + c=14 + 16+13.04=43.04$.

Answer:

less than 46 units