Trigonometry: Maths Diagnostic

\( \rm A \ right \ angled \ triangle \ has \ longest \ side \ length \ 16 \ cm \ and \ shortest \ side \ length \ 7 \ cm. \\ What \ is \ the \ angle \ between \ these \ two \ sides? \)

\( \rm {\it A} \ right \ angled \ triangle \ has \ three \ sides \ {\it A, \ B } \ and {\it\ C}. \ The \ angle \ between \ side \ {\it B} \ and \ {\it C} \ is \ a \ right \ angle \ and \\ the \ length \ of \ side \ {\it A} \ is \ 12 \ cm. \ Calculate \ the \ angle \ between \ side \ {\it A} \ and \ side \ {\it B}, \ if \ the \ length \ of \ side \ {\it C} \ is \ 8 \ cm. \)

\( \rm A \ right \ angled \ triangle \ has \ sides \ {\it X, \ Y} \ and \ {\it Z}, \ where \ {\it Z } \ is \ the \ hypotenuse \ and \ is \ 62 \ cm. \\ The \ angle \ between \ {\it X} \ and \ {\it Z} \ is \ 30 ^\circ ,\ what \ is \ the \ length \ of \ side \ {\it Y}\ ?\)

\( \rm{ A \ right \ angled \ triangle \ has \ shortest \ side \ 7 \ cm. \\ If \ the \ angle \ between \ the \ shortest \ side \ and \ the \ hypotenuse \ is \ 65^{\circ}, \ what \ is \ the \ length \ of \ the \ hypotenuse? } \)

\( \rm The \ two \ shortest \ sides \ of \ a \ right \ angled \ triangle \ are \ 9 \ cm \ and \ 11 \ cm. \\ What \ is \ the \ smallest \ of \ the \ internal \ angles? \)

\( \rm {One \ internal \ angle \ of \ a \ right \ angled \ triangle \ is \ 27 ^{\circ}. \\ What \ is \ the \ ratio \ of \ the \ shortest \ side \ to \ the \ longest \ side? } \)