Question

1. Find the missing side lengths of the special right triangles. Leave your answers as radicals in simplest form 30° 9​

Answer 1

Answer:

a = 18 units

b = 9√3 units

Step-by-step explanation:

By applying sine rule in the given triangle,

sin(30°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\frac{1}{2}=\frac{9}{a}$

a = 18 units

Now apply cosine rule in the given triangle,

cos(30°) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

$\frac{\sqrt{3}}{2}=\frac{b}{a}$

$\frac{\sqrt{3}}{2}=\frac{b}{18}$

b = $\frac{18\sqrt{3} }{2}$

b = $9\sqrt{3}$ units