IF a+b=90 degree AND b+c=a THEN WHAT
IS THE VALUE OF tan a.
IF a+b=90 degree AND b+c=a THEN WHAT
IS THE VALUE OF tan a. DO TRY!!!
Before I start, I must say I have found no
mathematical way to settle on just one set of values.
a + b = 90 b + c = a
b = 90 - a (90 - a) + c = a
90 + c = 2a
(b + c) + b = 90
2b + c = 90
We can keep manipulating these, but there
is no way to eliminate one of the variables so
we can zero in on another. So, let's make a table.
a |
b |
c |
2b |
a+b |
90+c |
2a |
89 |
1 |
88 |
2 |
90 |
178 |
178 |
88 |
2 |
86 |
4 |
90 |
176 |
176 |
87 |
3 |
84 |
6 |
90 |
174 |
174 |
86 |
4 |
82 |
8 |
90 |
172 |
172 |
85 |
5 |
80 |
10 |
90 |
170 |
170 |
84 |
6 |
78 |
12 |
90 |
168 |
168 |
83 |
7 |
76 |
14 |
90 |
166 |
166 |
82 |
8 |
74 |
16 |
90 |
164 |
164 |
81 |
9 |
72 |
18 |
90 |
162 |
162 |
We can extend that up to the point where b = 45,
49 |
41 |
8 |
82 |
90 |
98 |
98 |
48 |
42 |
6 |
84 |
90 |
96 |
96 |
47 |
43 |
4 |
86 |
90 |
94 |
94 |
46 |
44 |
2 |
88 |
90 |
92 |
92 |
45 |
45 |
0 |
90 |
90 |
90 |
90 |
It won't do any good to go beyond that because c becomes negative.
Formual 2b + c = 90. Add the entries in cols 3 and 4. Always works.
Formula 90 + c = 2a. Compare entries in cols 6 and 7. Always works.
Formula b + c = a. Add entries in cols 2 and 3, compare to col 1. Always works.
Formula a + b = 90. Add entries in cols 1 and 2. Always works.
The best we can do is decide "I want symmetry." So we choose 60 degrees for
a and 30 degrees for both b and c. Try them in every formula above; they work.
Using those choices, the tangent of a is 1.732.