IB MATH AI HL, Paper 2, May, 2021, TZ2, Solved Past Paper

Determine the measure of angle $(\mathrm{\angle }ACB)$.

This question is asking for the measurement of the angle formed at point (C) between points (A) and (B). You need to find the size of this angle in degrees or radians, depending on the context provided.

A town is planning to extend a highway, creating a segment that will pass through a field, intersecting at points D and E. It's known that the length from D to C is 210 meters and that the angle CED measures 100 degrees.

The objective is to determine the distance between D and E.

The local authorities are interested in transforming a triangular section of a farmer's land into a public parking space. This triangular section is denoted by DCE. In a fair exchange, the farmer will receive a new tract of land, triangle ADF, which has an equivalent size to triangle DCE, with the stipulation that point F is directly in line with points D and E.

The challenge lies in calculating the magnitude of the farmer's land that is up for exchange, essentially the area of triangle DCE.

Estimate the distance function (DF) considering that the highway has a width of zero.

This means you should calculate the distance function assuming the highway is a one-dimensional line.