Question

solve the triangle. round answers to two decimal places. enter the degree symbol by typing deg.

image of a triangle with vertices a, b, c and side lengths bc = 5, ac = 17, ab = 21

a) \\(m\angle a\\)

\\(m\angle a =\\)

b) \\(m\angle b\\)

\\(m\angle b =\\)

c) \\(m\angle c\\)

\\(m\angle c =\\)

Explanation:

Identificar los datos del triángulo

Dados los lados del triángulo \(ABC\):

• \(a = BC = 5\)
• \(b = AC = 17\)
• \(c = AB = 21\)

Calcular el ángulo A usando la Ley de Cosenos

$$ \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} = \frac{17^2 + 21^2 - 5^2}{2 \cdot 17 \cdot 21} = \frac{289 + 441 - 25}{714} = \frac{705}{714} \approx 0.98739 $$

$$ A = \arccos(0.98739) \approx 9.11^\circ $$

Calcular el ángulo B usando la Ley de Cosenos

$$ \cos(B) = \frac{a^2 + c^2 - b^2}{2ac} = \frac{5^2 + 21^2 - 17^2}{2 \cdot 5 \cdot 21} = \frac{25 + 441 - 289}{210} = \frac{177}{210} \approx 0.84286 $$

$$ B = \arccos(0.84286) \approx 32.56^\circ $$

Calcular el ángulo C usando la suma de ángulos internos

$$ C = 180^\circ - A - B = 180^\circ - 9.11^\circ - 32.56^\circ = 138.33^\circ $$

Answer:

Question a

\(m\angle A =\) <blank>\(9.11\text{ deg}\)</blank>

Question b

\(m\angle B =\) <blank>\(32.56\text{ deg}\)</blank>

Question c

\(m\angle C =\) <blank>\(138.33\text{ deg}\)</blank>