An engineer on the ground is looking at the top of a building. The angle of elevation to the top of a building is 38 degrees. The engineer knows the building is 300ft tall. What is the distance from the engineer to the base of the building to the nearest while foot?

Question

anonymous · Answer

38 degrees?give me a good figure

anonymous · Answer

Using the sine rule and assuming that the building is straight:
$$a/sinA = b/sinB = c/sinC$$
$$300/\sin38 = x/\sin(180-90-38) = x/\sin58$$
$$(300*\sin52)/\sin38 = x$$
$$x = 999 ft (3 s.f.)$$

anonymous · Answer

* = x/sin52

anonymous · Answer

My options are 
A) 234 ft
B) 384 ft
C) 185 ft
D) 487 ft

jim_thompson5910 · Answer

let x = distance from the engineer to the base of the building 


tan(38) = Height of Building/Distance Engineer is from building


tan(38) = 300/x


x*tan(38) = 300


x = 300/tan(38)


x = 300/0.7812856


x = 383.98250268


x = 384 (round to the nearest foot)


So the engineer is roughly 384 feet from the base of the building