Can someone help with 2 different geometry project. Show all work please!?

Question

A surveyor measures the angle of elevation to the top of a building to be 70°. q-he surveyor then walks 50 ft farther
from the base of the tower and measures the angle of elevation to be 50°. ~he surveyor’s angle-measuring device is 5.5 ft from the ground. How tall is the building, to the nearest foot?
Two observers simultaneously observe an airplane overhead
and between them. They measure their angle of elevation to the airplane and obtain 48° and 73°. rIhe airplane is 1.7 mi above the point shown in the figure. What are the distances, x and y, of each observer from the point directly below the airplane? Round your answers to the nearest hundredth of a mile

MechEng2030 · Answer

tan(70) = h/x
tan(50) = h/(x + 50)
(x + 50)tan(50) = xtan(70)
x = (50tan(50))/(tan(70) - tan(50)) = 38.3 ft
h = 38.3tan(70) = 105.2 ft
So height of building = 5.5 ft + 105.2 ft = 111 ft to the nearest ft.

Thomas · Answer

(h-5.5)/x=tan70  and (h-5.5)/(x+50)=tan50

xtan70=(x+50)tan50

xtan70=xtan50+50tan50

x(tan70-tan50)=50tan50

x=50tan50/(tan70-tan50)

x=38.3  using this x in (h-5.5)/x=tan70 gives

h=xtan70+5.5

h=111 ft.

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Can someone help with 2 different geometry project. Show all work please!?

2 Answers