3D Trigonometry Challenge: Angles in a Tetrahedron

[size=85][b][size=100][size=150]The diagram shows a tetrahedron with an equilateral triangular base.[br][/size][/size][/b][/size][b][size=100]The sides of the base are 8cm and the altitude of the tetrahedron is 10cm.[br][/size][/b][b]Point O is at the centre of the base and point S is the apex directly above the centre. [/b][size=85][size=150][size=200][size=100][b]Drag the sliders to see the measures from different perspectives.[br][/b][/size][size=100][b][color=#980000]Q1 Find the angle made with the base and an edge[br]Q2 Find the angle made with the base and a face.[/color][/b][br][b]Tick the HINTS boxes when required.[/b] [/size][size=100][b]Show all working. The solutions will be posted to teams later.[/b][/size][/size][/size][/size][size=150][size=200][b][justify][/justify][/b][/size][/size][size=150][size=200][b][justify][/justify][/b][/size][/size]

Information: 3D Trigonometry Challenge: Angles in a Tetrahedron