Given a = 8.1, b = 4.8, c = 5.5 What is tan B?

Question

Given a = 8.1, b = 4.8, c = 5.5

What is tan B?

Answer 1

By Cosine Law b² = a² + c² - 2a·c·cosB, from here cosB = (a² + c² - b²)/(2ac);

cosB = (8.1² + 5.5² - 4.8²)/(2·8.1·5.5) = 0.8173;

angle B is aqute angle as smallest angle in triangle(opposite angle to smallest side).

sinB = sqrt(1 - cos²B) = sqrt(1 - 0.8173²) = 0.5762;

Now we have: tanB = sinB/cosB = 0.5762/0.8173 = 0.7050;

Answer: tanB ≅ 0050

Answer 2

To get an angle one formula that sticks in my head is: alpha=acos((b^2+c^2-a^2)/(2bc).

The sides are labeled a=shortest; b=mid;c=hypotenuse. In this case a=4.8; b=5.5; c=8.1.

So: alpha=acos((5.5^2+8.1^2-4.8^2)/(2*5.5*8.1)=35.186............

beta=acos((a^+c^2-b^2)/(2ac)=41.32...........

gamma=180-α-β=180-35.186-41.32=103.493...............=γ

B in your case is α here; so tan=35.186=.705.................

side a opposite α

b β

c γ