Question

Instructions: Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. 163 30° y X

Answer 1

Based on the given information in the image, you have for x:

sin 30° = (16√3)/x solve for x

x = (16√3)/(sin 30°)

x = (16√3)/(1/2) = 32√3

To obtain the value of y, use the Pythagorean theorem:

x² = y² + (16√3)² solve for y and replace x

y² = x² - (16√3)²

y² = (32√3)² - (16√3)²

y² = 3072 - 768

y² = 2304

y = √2304

y = 48

Hence, you have:

x = 32√3

y = 48