see the attached figure to better understand the problem
we know that
in the right triangle ABC
cos 56°=AC/AB
where
AC is the adjacent side to angle 56 degrees------> the distance from the surveyor to the building
AB is the hypotenuse-----> 148 ft 2 in
56 degrees------> is the angle of elevation
so
cos 56°=AC/AB---------> solve for AC
AC=AB*cos 56°
AB=148 ft 2 in
convert 2 in to ft
1 ft -----> 12 in
x ft------> 2 in
x=2/12-----> x=0.17 ft
AB=148 ft 2 in-----> 148 ft+0.17 ft------> AB=148.17 ft
AC=AB*cos 56°----> AC=148.17*cos 56°------> AC=82.86 ft
convert 0.86 ft to in
0.86 ft=0.86*12-----> 10.32 in
distance AB=82 ft 10 in
the answer is
the distance from the surveyor to the building is 82 ft 10 in
we know that
m∠SQR+x= -------> by supplementary angles
so
m∠SQR=
The sum of the internal angles of a triangle is equal to degrees
m∠SQR+m∠QSR+m∠SRQ=
substitute the values in the formula
m∠SQR++
=
m∠SQR= degrees
<u>Find the value of x</u>
m∠SQR=
x=-m∠SQR
x=
x= degrees
therefore
<u>the answer is</u>
the value of x is degrees
