Questions: Solve the triangle shown to the right. A ≈ □, □, and C ≈ □ □° (Round to the nearest tenth as needed.)

Transcript text: Solve the triangle shown to the right. $A \approx$ $\square$ $\square$ ， and C $\approx$ $\square$ $\square^{\circ}$ (Round to the nearest tenth as needed.)

Solution

Solution Steps

Step 1: Identify the type of triangle

The given triangle has two sides of equal length (AC = AB = 14). This is an isosceles triangle.

Step 2: Find angle B

Since triangle ABC is isosceles with AC = AB, the angles opposite these sides are equal. Therefore, angle B is equal to angle C. Let's denote angle B as 'x'. We can use the Law of Cosines to find angle B:

b² = a² + c² - 2ac * cos(B)

17² = 14² + 14² - 2 * 14 * 14 * cos(x)

289 = 196 + 196 - 392 * cos(x)

289 = 392 - 392cos(x)

392cos(x) = 103

cos(x) = 103/392

x = arccos(103/392)

x ≈ 74.5°

Step 3: Find angle C

Since angle B is equal to angle C, angle C is also approximately 74.5°.

Step 4: Find angle A

The sum of the angles in a triangle is 180°. Therefore, angle A = 180° - angle B - angle C.