Question

select the correct answer.

rounded to the nearest tenth, what is the perimeter of the triangle?

• 9.3 centimeters
• 10.8 centimeters
• 11.0 centimeters
• 11.8 centimeters
• 16.2 centimeters

Explanation:

⚡ Using what you learned: right triangle trigonometry (soh cah toa)

Step 1: Identify the side lengths using trigonometry

Using the hypotenuse \( c = 5\text{ cm} \) and the angle \( 30^\circ \):

The side opposite to the \( 30^\circ \) angle (vertical leg, \( a \)):

$$ a = 5 \cdot \sin(30^\circ) = 5 \cdot 0.5 = 2.5\text{ cm} $$

The side adjacent to the \( 30^\circ \) angle (horizontal leg, \( b \)):

$$ b = 5 \cdot \cos(30^\circ) = 5 \cdot \frac{\sqrt{3}}{2} \approx 5 \cdot 0.866 = 4.33\text{ cm} $$

Step 2: Calculate the perimeter

Sum the three sides of the triangle:

$$ P = a + b + c $$

$$ P = 2.5 + 4.33 + 5 = 11.83\text{ cm} $$

Rounding to the nearest tenth gives \( 11.8\text{ cm} \).

Answer:

11.8 centimeters