Question

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

Explanation:

Step1: Find the other side - lengths using trigonometry

In a 30 - 60 - 90 right - triangle, if the hypotenuse $c = 5$ cm. The side opposite the 30° angle $a=\frac{c}{2}=\frac{5}{2}=2.5$ cm. The side opposite the 60° angle $b = a\sqrt{3}=2.5\sqrt{3}\approx2.5\times1.732 = 4.33$ cm.

Step2: Calculate the perimeter

The perimeter $P=a + b + c$. Substitute $a = 2.5$ cm, $b\approx4.33$ cm, and $c = 5$ cm into the formula. $P=2.5+4.33 + 5=11.83\approx11.8$ cm.

Answer:

C. 11.8 centimeters