Question

Given a triangle with side lengths 48 cm, 35 cm. Calculate the size of the angle at A.

A) 37.76 degrees
B) 49.32 degrees
C) 62.24 degrees
D) 72.18 degrees

Answer 1

D) 72.18 degrees to find the cosine of angle A using the given side lengths of the triangle, we derive the measure of angle A to be approximately 72.18 degrees.

Step-by-step explanation:

The angle at vertex A in the given triangle with side lengths of 48 cm, 35 cm can be calculated using the Law of Cosines. Applying this law, specifically the formula cos(A) =
`(b^2 + c^2 - a^2)`/ (2bc), where 'a', 'b', and 'c' represent the lengths of the sides opposite to angles A, B, and C, respectively. In this case, 'a' is unknown (angle at A), 'b' is 48 cm, and 'c' is 35 cm. After substituting the values into the formula, we can solve for the cosine of angle A and then find the angle by taking the inverse cosine.

Therefore, angle A ≈ 72.18 degrees.

By utilizing the Law of Cosines, specifically the equation to find the cosine of angle A using the given side lengths of the triangle, we derive the measure of angle A to be approximately 72.18 degrees. This mathematical approach provides a precise calculation of the angle based on the provided side lengths, confirming the angle at vertex A in the triangle.