Question

solve the triangle.
a = 15.0 ft, b = 17.0 ft, c = 19.0 ft

what is the measure of angle a?
a = \\(\square\\)°
(round to two decimal places as needed.)
what is the measure of angle b?
b = 58.60 °
(round to two decimal places as needed.)
what is the measure of angle c?
c = 72.54 °
(round to two decimal places as needed.)

Explanation:

Step1: Apply Law of Cosines for angle A

The Law of Cosines formula for angle \( A \) is \( \cos A=\frac{b^{2}+c^{2}-a^{2}}{2bc} \). Substitute \( a = 15.0 \), \( b = 17.0 \), \( c = 19.0 \):
\( \cos A=\frac{17.0^{2}+19.0^{2}-15.0^{2}}{2\times17.0\times19.0}=\frac{289 + 361-225}{646}=\frac{425}{646}\approx0.6579 \)

Step2: Find angle A

Take the arccosine: \( A=\arccos(0.6579)\approx48.86^{\circ} \)

Answer:

\( A = 48.86^{\circ} \)