Question 9, 7.3.35 Solve the triangle. \[ a=13.0 \mathrm{ft}, b=17.0 \mathrm{ft}, \mathrm{c}=29.0 \mathrm{ft} \] What is the measure of angle $A$ ? \[ A=\square^{\circ} \] (Round to two decimal places as needed.) What is the measure of angle $B$ ? \[ \mathrm{B}=\square^{\circ} \] (Round to two decimal places as needed.) What is the measure of angle $C$ ? \[ \mathrm{C}=\square^{\circ} \] (Round to two decimal places as needed.)

Step 1 ：Given the side lengths of a triangle as \(a = 13.0\) ft, \(b = 17.0\) ft, and \(c = 29.0\) ft.

Step 2 ：Calculate the measure of angle A using the formula \(\cos A = \frac{b^2 + c^2 - a^2}{2bc}\). Substituting the given values, we get \(\cos A = 0.9746450304259635\).

Step 3 ：Convert the cosine value to an angle by taking the arccosine. This gives \(A = 0.22566721395074552\) radians.

Step 4 ：Convert the angle from radians to degrees to get \(A = 12.92977893385349\) degrees.

Step 5 ：Calculate the measure of angle B using the formula \(\cos B = \frac{a^2 + c^2 - b^2}{2ac}\). Substituting the given values, we get \(\cos B = 0.9562334217506632\).

Step 6 ：Convert the cosine value to an angle by taking the arccosine. This gives \(B = 0.2969498602293602\) radians.

Step 7 ：Convert the angle from radians to degrees to get \(B = 17.013973718142037\) degrees.

Step 8 ：Calculate the measure of angle C using the formula \(\cos C = \frac{a^2 + b^2 - c^2}{2ab}\). Substituting the given values, we get \(\cos C = -0.8665158371040724\).

Step 9 ：Convert the cosine value to an angle by taking the arccosine. This gives \(C = 2.618975579409687\) radians.

Step 10 ：Convert the angle from radians to degrees to get \(C = 150.05624734800446\) degrees.

Step 11 ：The measures of the angles are approximately \(A = \boxed{12.93^{\circ}}\), \(B = \boxed{17.01^{\circ}}\), and \(C = \boxed{150.06^{\circ}}\).