An oak tree is 12 feet tall and a bird is standing on the ground 16 feet from the tree. If the bird flies directly to the top of the tree, how far will it fly?

20 ft.

Step-by-step explanation:

There are two different (yet similar) ways to solve this problem:

a. Pythagorean theorem

b. Pythagorean triplet recognition

With option "a", you set it up:

12² + 16² = x²

144 + 256 = x²

400 = x²

x = 20

But, the arguably "easier" way to find out the distance is to use the Pythagorean's triplet recognition.

We know that the most common right triangle is the 3-4-5 right triangle.

If you take the three side lengths, and multiple them by the same thing, those are the sides to another right triangle.

ex. 3-4-5  *   5

15-20-25 are the sides of another right triangle!

This also means that if you have a triangle that has the sides 15, 20, and 25, you immediately know it's a right triangle.

When we look at 12 and 16, we know they are the legs of the triangle.

We also know that if we multiply 4 times 3 and 4, it will equal 12 and 16.

So what's 5 times 4? 20!

i am thinking c. sorry if im wrong .

step-by-step explanation:

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47