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Answer :
Approximating to the nearest integer, we get, c ≈ 25 inches. Hence, the correct option is d. 35 pulgadas.
Given that in the triangle △ABC, ∠A = 105∘ , ∠B = 30∘ and b = 25 inches. To find: The measure of c rounded to the nearest integer. In order to solve this problem, we will use the law of sines which states that, a/sinA = b/sinB = c/sinC where a, b and c are sides of the triangle and A, B, and C are the opposite angles. So, we can write,
sinC = (c/sinC) x sinC = (c/sinC) x sinA/sinA = a/sinA
Also, we know that sum of all angles of a triangle is 180°.
Therefore, ∠C = 180° - ∠A - ∠B = 180° - 105° - 30° = 45° Thus, sin C = sin45° = √2/2 Therefore, c/sinA = √2/2c = (sinA/√2) x c
Substituting values of sinA and c, we get, c = (sin105/√2) x 25 = 24.55 inches
Approximating to the nearest integer, we get, c ≈ 25 inches. Hence, the correct option is d. 35 pulgadas.
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