select the correct answer. rounded to the nearest tenth, what is the perimeter of the triangle? 60° 5 cm 30°…

Explanation:

Step1: Find the side opposite the 30 - degree angle

In a 30 - 60 - 90 triangle, if the hypotenuse $c = 5$ cm, and the side opposite the 30 - degree angle $a$ is related to the hypotenuse by $a=\frac{c}{2}$. So $a=\frac{5}{2}=2.5$ cm.

Step2: Find the side opposite the 60 - degree angle

The side opposite the 60 - degree angle $b$ is given by $b = a\sqrt{3}$. Since $a = 2.5$ cm, then $b=2.5\sqrt{3}\approx2.5\times1.732 = 4.33$ cm.

Step3: Calculate the perimeter

The perimeter $P$ of a triangle is $P=a + b + c$. Substitute $a = 2.5$ cm, $b\approx4.33$ cm, and $c = 5$ cm. So $P=2.5+4.33 + 5=11.83$ cm.

Step4: Round to the nearest tenth

Rounding 11.83 to the nearest tenth gives 11.8 cm.

Answer:

D. 11.8 centimeters