Question

Use the ratio of a 30-60-90 triangle to solve for the variables. Leave your answers as radicals in simplest form. x= y=

Answer 1

Answer:

x = 10 units, y = 5 units

Step-by-step explanation:

Given triangle ABC is a 30-60-90 triangle,

m∠C = 60°

By applying Sine rule in the given triangle,

Sin(60)°= $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Sin(60)° $=\frac{\text{AB}}{\text{AC}}$

$\frac{\sqrt{3}}{2}=\frac{\text{AB}}{\text{AC}}$

$\frac{\sqrt{3}}{2}=\frac{5\sqrt{3}}{x}$

x = 10 units

Similarly, by applying Cosine rule in the given triangle,

Cos(60)° = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

Cos(60)° = $=\frac{\text{BC}}{\text{AC}}$

$\frac{1}{2}=\frac{y}{x}$

y = $\frac{x}{2}$

y = 5 units

Therefore, x = 10 units and y = 5 units will be the answer.