A farmer notes that in a field full of horses and geese there are 36 heads and 106 feet. How many of each animal are there?

17 horses and 19 geese

Step-by-step explanation:

Let x be the number of horses and y be the number of geese

We know that, horses have four feet and geese have 2 feet

It is given that

x+y=36 (i)

and

4x+2y=106 (ii)

Solve the two equations simultaneously by substitution,

From equation (i)

y=36-x (iii)

Substitute y with 36-x in equation (ii)

4x+2(36-x)=106

4x+72-2x=106

4x-2x=106-72

2x=34

x=17

Then

Substitute x=17 to equation (iii)

y=36-17=19

x=17, y=19

We therefore have 17 horses and 19 geese

sin x° = opposite ÷ hypotenuse

Step-by-step explanation:

Recall the mnemonics SOHCAHTOA,

The meaning is as follows;

SOH

↓

CAH

↓

TOA

↓

Therefore the last choice is correct.