Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Using the technique in the model above, find the missing sides in this 30°-60°-90° right triangle.



Hypotenuse = 12

Long =

Answer 1

It will also be 12 long

Answer 2

Answer:

$\text{Long}=6\sqrt{3}\ units$

$\text{Short}=6\ units$

Step-by-step explanation:

We are given a right angled triangle such that the hypotenuse of this triangle is:

Hypotenuse= 12 units

Also, the side long is the side adjacent to the angle 30°.

This means that in order to find this side long we need to use the cosine trignometric ratio.

i.e.

$\cos 30=\dfrac{long}{Hypotenuse}\\\\i.e.\\\\\cos 30=\dfrac{long}{12}\\\\i.e.\\\\\dfrac{\sqrt{3}}{2}=\dfrac{long}{12}\\\\i.e.\\\\long=6\sqrt{3}\ units$

and the side short is calculated by using sine ratio corresponding to angle 30°.

i.e.

$\sin 30=\dfrac{short}{Hypotenuse}\\\\i.e.\\\\\dfrac{1}{2}=\dfrac{short}{12}\\\\i.e.\\\\short=\dfrac{12}{2}\\\\i.e.\\\\short=6\ units$