Question

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

Long = 3

Hypotenuse =

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

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

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)=(BC)/(AC)`

`(\sqrt3)/(2)=(3)/(AC)`

`AC=3* (2)/(\sqrt3)=2\sqrt3 units`

`\sin 30=(AB)/(AC)=(AB)/(2\sqrt3)`

`(1)/(2)=(AB)/(2\sqrt3)`

`AB=\sqrt3units`

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