In triangle ABC with side lengths AB = 17.5, AC = 15.8, and BC = 25.4, what is the measure of angle A?

a) 38.2 degrees
b) 53.7 degrees
c) 71.1 degrees
d) 96.9 degrees

Question

High School

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Answer :

rubygupta rubygupta · Answer 1 · 2025-03-09T21:41:14-04:00

Calculate the measure of angle A in a triangle using the Law of Cosines formula with given side lengths. Therefore the correct answer is: A)

"Angle" typically refers to the geometric figure formed by two rays or lines that extend from a common point. Here are some key points about angles:

Vertex: The common endpoint where the two rays meet is called the vertex of the angle.

Measure: Angles are usually measured in degrees, where a full rotation around a point is 360 degrees.

Types of Angles:

Acute Angle: An angle that measures less than 90 degrees.

Right Angle: An angle that measures exactly 90 degrees. It forms a perfect "L" shape.

Obtuse Angle: An angle that measures more than 90 degrees but less than 180 degrees.

Straight Angle: An angle that measures exactly 180 degrees. It forms a straight line.

Reflex Angle: An angle that measures greater than 180 degrees but less than 360 degrees.

Full Angle: An angle that measures exactly 360 degrees. It represents a full rotation.

The measure of angle A in triangle ABC can be calculated using the Law of Cosines formula:

Cos(A) = (b^2 + c^2 - a^2) / (2*b*c)

Plugging in the given side lengths:

Calculate Cos(A) = (15.8^2 + 25.4^2 - 17.5^2) / (2*15.8*25.4)

Find the inverse Cosine to get the angle A

The measure of angle A in triangle ABC is approximately 38.2 degrees.