23.03.2023 - 14:32

Solve for x in the triangle. Round your answer to the nearest tenth.

Solve for x in the triangle. Round your answer to the nearest tenth.

Answers (1)
  • AcidDreams
    April 7, 2023 в 17:43

    To solve for x in the triangle, we can use the Law of Cosines, which relates the side lengths of a triangle to the cosine of one of its angles.

    In this case, we can use the Law of Cosines to solve for side AB, since we know the lengths of sides AC and BC and the measure of angle C:

    AB^2 = AC^2 + BC^2 - 2(AC)(BC)cos(C)

    Plugging in the given values, we get:

    AB^2 = 10^2 + 8^2 - 2(10)(8)cos(35)

    Simplifying and taking the square root, we get:

    AB ≈ 8.4

    Now that we know the length of side AB, we can use the Law of Cosines again to solve for angle A:

    cos(A) = (AB^2 + AC^2 - BC^2) / (2ABAC)

    Plugging in the values we know, we get:

    cos(A) = (8.4^2 + 10^2 - 8^2) / (2 * 8.4 * 10)

    Simplifying, we get:

    cos(A) ≈ 0.668

    Taking the inverse cosine (cos^-1) of both sides, we get:

    A ≈ 47.5 degrees

    Therefore, the measure of angle A is \approx imately 47.5 degrees.

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