IB Maths AI HL Topic 3: Geometry and trigonometry questions

A survey team is preparing a map of a coastal reserve. In one triangulation, stations $A$ and $B$ are $138\text{ m}$ apart. The measured angles in triangle $ABP$ are $\angle BAP=52^\circ$ and $\angle ABP=67^\circ$

A second mapped zone is represented by triangle $XYZ$ where $XY=84\text{ m}$ $XZ=117\text{ m}$ and $\angle YXZ=42^\circ$

An architect models a rectangular atrium as a cuboid measuring $8\text{ m}$ by $6\text{ m}$ on the floor and $9\text{ m}$ high. Let $A=(0,0,0)$ be one lower corner and $G=(8,6,9)$ the opposite upper corner, with coordinates in metres and the floor in the plane $z=0$

Figure 1 shows a line segment $AB$ on a Cartesian grid.

A flat map uses Cartesian coordinates to locate radio beacons. The segment $AB$ lies on the line $3x-4y-10=0$ and its midpoint is $M(2,-1)$