Trigonometry help!!!!!!!!!!!!!!!

Question

In the triangle ABC, if side a is 3, side b is 4 and side c is 5, what is the cosine of the smallest angle?

Answer 1

Given that side a is 3, side b is 4 and side c is 53

Find the largest angle of the triangle first. This will be / C because the longest side is C.

Law of cosines: c² = a² + b² -2abcosC

5² = 3² + 4² - 2(3)(4)cosC.

25 = 9 + 16 - 24cosC

25 = 25 - 24cosC

Subtract 25 from each side.

-24cosC = 0

Divide each side by -24.

cosC = 0

Trigonometric table in cos90° = 0

cosC = cos90 then /C = 90°

Now that we have an angle, we can switch to the law of sines.

Find / B: sinB/b = sinC/c

sinB/4 = sin90/5

sinB/4 = 1/5

Multiply each side by 4.

sinB = 4/5 = 0.8

Trigonometric table in sin53° = 0.8

sinB = sin53° then /B = 53°

Total of the three angles in the triangle is 180°.

So, A+B+C = 180°

Substitute C = 90° and B = 53° in the equation.

A + 53° + 90° = 180°

A + 143° = 180°

Subtract 143° from each side.

/A = 37°

Therefore /A = 37°, /B = 53° and /C = 90°.