trigonometry?

Question

ABC-is a triangle(angle c=90 degrees)
BC=6
AC=7
calculate the angles of the triangle.
I just started learning trigonometry so please give detailed way

Answer 1

tan B = 7 / 6
B = 49.4 °
A = 40.6 °
C = 90 °

Answer 2

Step 1:
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let's assume a smaller triangle Abc that
1/ shares the point A with the triangle ABC
2/ where b is on the segment AB
3/ where c is on the segment AC
4/ where c=90 degrees
5/ where Ab=1
(I strongly suggest you do the drawing and notice that the Abc triangle is a scaled down version of the larger triangle ABC:)

In this case per definition
Ac=cosine(AngleA)
bc=sine(AngleA)
bc/Ac=tangent(AngleA)

AngleA= Arc-Tangent(bc/Ac)

Step 2:
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Since the triangle Abc is a scaled down version of the triangle ABC we can assume that there is number (let's call it is S for scaling factor) such as:

AB=S*Ab
AC=S*Ac
BC=S*bc

Hence:
AngleA= Arc-Tangent(bc/Ac)
= Arc-Tangent((BC/S) /( AC/S))

We multiply by S on both numerator and denominator and we get

AngleA= Arc-Tangent((BC) /( AC))
=Arc-Tangent(7/6)
You take your calculator and you get Angle A= 49 degrees

Step 3:
=====
In a triangle the sum of the 3 angles = 180 degrees hence
AngleA+AngleB+AngleC=180 degrees

or AngleB=180 degrees -Angle A -Angle C
=180-49-90
=41 degrees

Answer 3

solve for A first

tan^-1 = 6/7 (since 6 is the opposite side of angle A and 7 is adjacent and tangent is opposite/adjacent)
tan^-1=0.857142857
A=40.60 degrees

solve for B
B = 180 - (90 + 40.60)
B = 49.4 degrees

Answer 4

The easiest way would be to use pythagoream's formula:

a^2 + b^2 = c^2

In this case you have 6^2 + 7^2 = c^2

Answer 5

We'll find the angle a, based on this triangle:
http://math.colgate.edu/~kellen/interspace/tan67.gif

Then we know:

tan(a) = 6/7
a = arctan(6/7) = 40.6013 degrees (approx)

Which means

b = 90 - a = 49.3987 (approx)