Bob is told that the pitch on the roof of his garage is 5-12, meaning that for every 5 feet the roof increases vertically, it increases 12 feet horizontally. if θ is defined as the angle at the corner of the roof formed by the pitch of the roof and a horizontal line, what is sinθ?

Step-by-step explanation:

step 1

Find the hypotenuse of the right triangle with legs of 5 ft and 12 ft

Applying the Pythagoras Theorem

Let

d ----> the length of the hypotenuse

step 2

Find the sine of angle theta

Remember that

The sine of angle theta is equal to divide the opposite side of angle theta (5 feet) by the hypotenuse (13 feet)

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for