You can conclude that AE = DE because the triangles are about equal
Tan ( a + b ) = [ tan a + tan b ] / [ 1 - (tan a)*(tan b) ];
let be a = 2x and b = x;
=> tan 3x = [ tan 2x + tan x ] / [ 1 - (tan 2x)*(tan x) ] => (tan 3x)*[ 1 - (tan 2x)*(tan x) ] =
tan 2x + tan x => tan3x - tan 3xtan 2xtanx = tan 2x + tan x => <span> tan 3x−tan 2x−tanx = tan 3xtan 2xtanx.</span><span />
This is a right angle triangle.
So, by Pythagoras theorem,
√(32^2+20^2) = x
or √(1024+400) = x
or √1424 = x
or <em>37.74 = x</em>
The equation for the nth term in the arithmetic sequence is 8n + 8.
The number of people that can be accommodated in the 16th row is 136.
<h3>What is an
arithmetic progression?</h3>
Arithmetic Progression (AP) is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value. It is also called Arithmetic Sequence.
Given that,
No. of seats in first row = 16
No. of seats in second row = 24
No. of seats in third row = 32
Total number of rows = 50
It forms an arithmetic progression
First term = a = 16
common difference d = 8
Number of terms, n = 50
(A) The formula for the n th term of an arithmetic progression is given by
Tn = a + (n - 1) d
= 16 + (n-1) 8
= 16 + 8n - 8
Tn = 8n + 8
(B) Now,
n = 16
The number of seats in 16 th row is given by
T(16) = 8 x 16 + 8
T(16) = 136 seats
Hence, (A)The equation for the nth term in the arithmetic sequence is 8n + 8. and (B) The number of people that can be accommodated in the 16th row is 136.
To learn more about arithmetic progression from the given link:
brainly.com/question/24205483
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