Answer:
17.1 degrees
Step-by-step explanation:
The complete question in the attached figure
step 1
Find the length side of the diagonal AC in rectangle ABCD
Applying the Pythagorean Theorem
[tex]AC^2=AB^2+BC^2[/tex]
substitute the given values
[tex]AC^2=60^2+80^2[/tex]
[tex]AC^2=10,000\\AC=100\ cm[/tex]
step 2
Find the length side RC in the right triangle BRC
we know that
[tex]tan(21^o)=\frac{RC}{BC}[/tex] ----> by TOA (opposite side divided by adjacent side)
substitute the given values
[tex]tan(21^o)=\frac{RC}{80}[/tex]
[tex]RC=tan(21^o){80}[/tex]
[tex]RC=30.71\ cm[/tex]
step 3
Calculate the angle that AR makes with the horizontal plane ABCD
In the right triangle ARC
we know that
[tex]tan(\angle RAC)=\frac{RC}{AC}[/tex] ----> by TOA (opposite side divided by adjacent side)
substitute the given values
[tex]tan(\angle RAC)=\frac{30.71}{100}[/tex]
[tex]\angle RAC=17.1^o[/tex]
