Question

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

Answer 1

Answer:

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°

Step-by-step 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,

$\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}$

$\frac{a}{sinA}=\frac{b}{sinB}$

$\frac{34}{sin46}=\frac{27}{sinB}$

sinB = $\frac{27\times sin46}{34}$

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°

$\frac{b}{sinB}=\frac{c}{sinC}$

$\frac{27}{sin34.83}=\frac{c}{sin99.17}$

$\frac{27}{0.5711}=\frac{c}{0.9872}$

c = $\frac{27\times 0.9872}{0.5711}=46.67$

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°

Answer 2

Find the length of the hypotenuse

34^2 + 27^2 = c^2

1156 + 729 = 1885

c^2 = 1885

sqrt(1885)

c = 43.42