What is the length of side a? Round to the nearest tenth of an inch.

14.4 in.

Step-by-step explanation:

Given:

Base of a right triangle = 7 in

Height of a right triangle = a

Hypotenuse = 16 in

To find:

The length of side a.

Solution:

Using Pythagoras theorem:

In right triangle, square of the hypotenuse is equal to the sum of the squares of the other two sides.

Subtract 49 from both sides.

Taking square root on both sides, we get

a = 14.4

The length of side a is 14.4 in.

, 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