A shelf that is 19 cm wide is held up by a triangular bracket. The bracket makes a 40.1° angle with the bottom of the shelf. What is the height of the bracket?
12.24 cm
14.53 cm
13.19 cm
16 cm
To find the height of the bracket, we can use trigonometry. The height of the bracket forms the opposite side of the triangle, while the width of the shelf forms the adjacent side. We can use the tangent function to find the height:
tan(angle) = opposite / adjacent
tan(40.1°) = height / 19 cm
height = tan(40.1°) * 19 cm
height ≈ 14.53 cm
So the height of the bracket is approximately 14.53 cm. Therefore, the correct option is:
14.53 cm