Question

using special triangle rules, what is the length of side x? 2 30° a 2√3 b 2√2 c 2 d 4 8 using special triangle rules, what is the length of side x? 5 45° a 5 b 5√2 c 5√3 d 25

Explanation:

Step1: Identify the special - triangle rule for the first triangle

The first triangle is a 30 - 60 - 90 triangle. In a 30 - 60 - 90 triangle, if the side opposite the 30 - degree angle is $a$, the hypotenuse $c$ is related to the side opposite the 30 - degree angle by the formula $c = 2a$. Here, the side opposite the 30 - degree angle is 2, and $x$ is the hypotenuse.

Step2: Calculate the length of $x$ in the first triangle

Using the formula $x = 2\times2=4$.

Step3: Identify the special - triangle rule for the second triangle

The second triangle is a 45 - 45 - 90 triangle. In a 45 - 45 - 90 triangle, if the length of each of the legs is $a$, the length of the hypotenuse $x$ is given by $x=a\sqrt{2}$. Here, $a = 5$.

Step4: Calculate the length of $x$ in the second triangle

Using the formula $x = 5\sqrt{2}$.

Answer:

For the first triangle: D. 4
For the second triangle: B. $5\sqrt{2}$