Question

math 2 unit 3 quiz - version 1
right triangle trigonometry

1. solve for the missing leg of the right triangle.

118² + b² = 152²
name: thiago gonzalez

Explanation:

Step1: Set up the Pythagorean theorem.

Let the missing side be $b$. The Pythagorean theorem for a right - triangle is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a, b$ are the legs. Here $a = 118$, $c=152$. So we have the equation $118^{2}+b^{2}=152^{2}$.

Step2: Calculate the squares.

$118^{2}=118\times118 = 13924$ and $152^{2}=152\times152=23104$. The equation becomes $13924 + b^{2}=23104$.

Step3: Solve for $b^{2}$.

Subtract 13924 from both sides of the equation: $b^{2}=23104 - 13924$. So $b^{2}=9180$.

Step4: Solve for $b$.

Take the square root of both sides. Since $b$ represents the length of a side of a triangle, we take the positive square root. $b=\sqrt{9180}\approx95.81$.

Answer:

$b\approx95.81$