IB Maths AI HL AI 3.1 Trigonometry and 3D geometry 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 $z=0$

A mapping team approximates a wetland by triangle $ABC$ The horizontal distance between survey stations $A$ and $B$ is $1.80\text{ km}$ The measured interior angles are $\angle BAC=52.6^\circ$ and $\angle ABC=68.3^\circ$

The wetland qualifies for a reserve if its mapped area is at least $1.20\text{ km}^2$

A surveyor uses triangulation to estimate the area of a triangular wetland $ABC$ Points $A$ and $B$ lie on an accessible straight bank, and $AB=d$ metres. The measured interior angles are $\angle BAC=48^\circ$ and $\angle ABC=67^\circ$