Question

The curved line on the first quadrant intersects both the x and y axes. A right triangle is formed by drawing a line from the origin point upper X to point upper Y on the curved line. This line, line upper X upper Y, forms the hypotenuse of the triangle. From point upper Y, a perpendicular line is drawn downward to meet the x-axis at vertex upper Z. This line, line upper Y upper Z, is the right perpendicular side, which is marked by a small square. The x-axis from vertex upper X to vertex upper Z forms the base of the triangle. The angle between the x-axis and the hypotenuse at vertex upper X is start fraction pi over 3 end fraction. The hypotenuse upper X upper Y is labeled 1. The vertical leg upper Y upper Z is labeled start fraction start root 3 end root over 2 end fraction. The horizontal leg upper X upper Z is labeled start fraction 1 over 2 end fraction. The coordinates of vertex upper Y are left parenthesis start fraction 1 over 2 end fraction comma start fraction start root 3 end root over 2 end fraction right parenthesis.

Use the triangle shown on the unit circle to find tanπ3
.

(1 point)
Responses

3–√

Start Root 3 End Root

3√2

Start Fraction Start Root 3 End Root over 2 End Fraction

12

Start Fraction 1 over 2 End Fraction

1

Answer 1

tan(π/3) = opposite/adjacent = (√3/2) / (1/2) = √3.