Question

4. Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.

a= 8.1 in
b= 13.3 in
c= 16.2 in

ANSWERS:
1. A = 27.9°, B=54.8°, C=97.3°
2. A = 29.9°, B=54.8°, C=95.3°
3. No triangle satisfies the given conditions
4. A= 31.9°, B=52.8°, C=95.3°

Answer 1

To determine the missing parts of the triangle, we can use the law of cosines, which states that for a triangle with sides of lengths a, b, and c and angles opposite those sides of A, B, and C, respectively:

c^2 = a^2 + b^2 - 2ab cos(C)

b^2 = a^2 + c^2 - 2ac cos(B)

a^2 = b^2 + c^2 - 2bc cos(A)

Using the given values of a, b, and c, we can solve for the angles A, B, and C.

a = 8.1 in

b = 13.3 in

c = 16.2 in

c^2 = a^2 + b^2 - 2ab cos(C)

cos(C) = (a^2 + b^2 - c^2) / (2ab)

cos(C) = (8.1^2 + 13.3^2 - 16.2^2) / (2 * 8.1 * 13.3)

cos(C) = 0.421

C = cos^-1(0.421)

C ≈ 97.3°

b^2 = a^2 + c^2 - 2ac cos(B)

cos(B) = (a^2 + c^2 - b^2) / (2ac)

cos(B) = (8.1^2 + 16.2^2 - 13.3^2) / (2 * 8.1 * 16.2)

cos(B) = 0.268

B = cos^-1(0.268)

B ≈ 54.8°

We can find angle A by using the fact that the sum of the angles in a triangle is 180°:

A = 180° - B - C

A = 180° - 54.8° - 97.3°

A ≈ 27.9°

Therefore, the missing parts of the triangle are:

A ≈ 27.9°

B ≈ 54.8°

C ≈ 97.3°

So, the answer is option 1.