Question

Using the technique in the model above, find the missing sides in this 30°-60°-90° triangle.

Answer 1

For this case what you should do is use the following trigonometric relationship:
 sin (x) = C.O / h
 Where
 x: angle
 C.O: opposite leg
 h: hypotenuse
 Substituting the values we have:
 sen (60) = long / h
 sen (60) = 3 / h
 h = 3 / sin (60)
 h = 3.46
 Answer:
 h = 3.46

Answer 2

Answer:

$\text{The length of hypotenuse and short side is }2\sqrt3 units\text{ and }\sqrt3units$

Step-by-step explanation:

Given the figure

we have to find the missing sides in  30°-60°-90° triangle.

Long side=3 units

we have to find the length of short side and length of hypotenuse.

By trigonometric ratios

$\cos 30^{\circ}=\frac{BC}{AC}$

$\frac{\sqrt3}{2}=\frac{3}{AC}$

$AC=3\times \frac{2}{\sqrt3}=2\sqrt3 units$

$\sin 30=\frac{AB}{AC}=\frac{AB}{2\sqrt3}$

$\frac{1}{2}=\frac{AB}{2\sqrt3}$

$AB=\sqrt3units$

$\text{The length of hypotenuse and short side is }2\sqrt3 units\text{ and }\sqrt3units$