Answer:

Step-by-step explanation:
Given
sinΘ =
= 
Then the hypotenuse = 5 and one leg of the right triangle is 3
Using Pythagoras' identity to find the second leg (x)
x² + 3² = 5²
x² + 9 = 25 ( subtract 9 from both sides )
x² = 16 ⇒ x = 4
cosΘ =
= 
Answer:
4. (2^6)^-5.
an number to an exponent to another exponent is multiplied
Answer:
Total number of ways to distribute the prize = 2187

Step-by-step explanation:
Given:
Number of prizes = 7
Number of peoples = 3
We need to find the total number of ways to distribute the prize.
Solution:
From the above statement, 7 prizes are to be distributed between 3 people, wherein each person gets at least one prize.
Each prize is to be distributed among three persons. When the first prize is to be awarded, one of the three is chosen to win the prize. When the second prize is to be awarded, there are again three choices.
So, total number of distribution of the prizes is given as:


Therefore, total number of ways to distribute the prizes = 2187
The explanation is on the picture I attached!
Hope you get it!