If the length of side a is 12 centimeters, m
∠b
= 36°, and m
∠c
= 75°, what is the length of side b? round your response to two decimal places.

  b = 7.56 cm  .


All angles in a triangle add up to 180 ;

so m∠A = 180 - (75 + 36) = 180 - 111 = 69 ;

Note:  The law of sines:

(sin A) / a = (sin B) / b = (sin C) / C.

We have solved for m∠A ; which is:  69;

(sin A) / a = (sin B) / b ;  solve for "b" ;

(sin A) / a = (sin 69) / 12 cm  ;

(sin B) / b = (sin 36) / b ;  solve for "b" .

(sin 69) / 12 cm = (sin 36) / b ; solve for "b" ;

b sin 69 = 12 sin 36 ; 

Divide each side of the equation by "sin 69" ; to isolate "b" on one side of the equation; and to solve for "b" ;


    {b sin 69} / sin 69 = {12 sin 36} / sin 69 ;

            b =  (12 sin 36) / sin 69 = 7.5552387639166787

   b = 7.56 cm .

16 minutes is correct

, and

for

step-by-step explanation:

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

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

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