Question

unit exam - right triangles and trigonometry
find the value of x.
7
14
x = ?√

Explanation:

Step1: Apply Pythagorean theorem

For a right triangle, $a^2 + b^2 = c^2$, where $c$ is the hypotenuse. Here, $a=7$, $b=x$, $c=14$, so:
$$7^2 + x^2 = 14^2$$

Step2: Calculate squared terms

Compute the known squares:
$$49 + x^2 = 196$$

Step3: Isolate $x^2$

Subtract 49 from both sides:
$$x^2 = 196 - 49 = 147$$

Step4: Solve for $x$

Take the square root and simplify:
$$x = \sqrt{147} = \sqrt{49 \times 3} = 7\sqrt{3}$$

Answer:

$x = 7\sqrt{3}$