What is the length of the long leg in the right triangle shown below ?

The answer to your question is: length = 10.4 units

Step-by-step explanation:

Data

It's a right triangle with angles 30°- 60°- 90°

I'll solve this exercise with the function sine and cosine

a)    sin 60 = long leg / hypotenuse

      long leg = hypotenuse x sin 60

      long leg = 12 x 0.87

      lon leg = 10.4 units

b) cos 30 = long leg / hypotenuse

   long leg = hypotenuse x cos 30

   long leg = 12 x 0.87

   long leg = 10.4 units

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1