Question

Solve the triangle. A = 46°, a = 34, b = 27

Answer 1

Find the length of the hypotenuse

34^2 + 27^2 = c^2

1156 + 729 = 1885

c^2 = 1885

sqrt(1885)

c = 43.42

Answer 2

All sides of the triangle are a = 34, b = 27 and c = 46.7

and angles are A = 46°, B = 34.83° and C = 99.17°

Explanation:

In a given triangle A = 46°, a = 34 units and b = 27 units

Then we have to find all angles and measure of the side left.

By sine rule,

`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`

`(a)/(sinA)=(b)/(sinB)`

`(34)/(sin46)=(27)/(sinB)`

sinB =
`(27* sin46)/(34)`

sinB = 0.5712

B =
`sin^(-1)(0.5712)`

B = 34.83°

Since in a triangle,

∠A + ∠B + ∠C = 180°

46°+ 34.83° + ∠C = 180°

80.83° + ∠C = 180°

∠C = 180 - 80.83 = 99.17°

`(b)/(sinB)=(c)/(sinC)`

`(27)/(sin34.83)=(c)/(sin99.17)`

`(27)/(0.5711)=(c)/(0.9872)`

c =
`(27* 0.9872)/(0.5711)=46.67`

Therefore, all sides of the triangle are a = 34, b = 27 and c = 46.7

and angles are A = 46°, B = 34.83° and C = 99.17°