Given , , and , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Question

Given  ,  , and  , use the Law of Sines to solve the triangle for the value of a. Round answer to two decimal places.

Quizplus · Accepted Answer

We can start by identifying the sides opposite the angles using the given values. Let A, B, and C be the angles of the triangle, and let a, b, and c be the lengths of the sides opposite A, B, and C, respectively. Then, we have:

Angle A is opposite side 11ec1854_fd53_8034_acfc_3f94edbfe867_TBX8702_00 (which we will call c)
Angle B is opposite side 11ec1854_fd53_5921_acfc_eb10388c9fc4_TBX8702_11 (which we will call a)
Angle C is opposite side 11ec1854_fd53_8032_acfc_8100bff1377b_TBX8702_11 (which we will call b)

Now, we can use the Law of Sines, which states:

a/sin(A) = b/sin(B) = c/sin(C)

We want to solve for a, so we can rewrite this as:

a = b(sin(A)/sin(B)) = c(sin(A)/sin(C))

Plugging in the given values, we get:

a = 11ec1854_fd53_5921_acfc_eb10388c9fc4_TBX8702_11(sin(11ec1854_fd53_8034_acfc_3f94edbfe867_TBX8702_00)/sin(11ec1854_fd53_8032_acfc_8100bff1377b_TBX8702_11))

Using a calculator to evaluate this expression, we get:

a ≈ 11ec1854_fd53_8037_acfc_cf462c6c9fda_TBX8702_11

Rounding this to two decimal places, we get:

a ≈ 11ec1854_fd53_8037_acfc_cf462c6c9fda_TBX8702_11

Therefore, the best choice is C.

Given , , and , Use the Law