Pierre lives in a tall apartment building. He looks out his window and spots a car on the road that runs straight toward his building. His angle of depression to the car is 21°.
Pierre looks farther down the road and spots a dump truck. He estimates that the car is 600 feet in front of the dump truck. His angle of depression to the dump truck is 14°.
How far above the ground is Pierre's line of sight?
approximately 145.2 feet
approximately 288.1 feet
approximately 373.3 feet
approximately 426.8 feet
How far above the ground is Pierre's line of sight?
Hello Guest!
\(C=h\cdot tan(90-21)\\ DT=h\cdot tan(90-14)\\ DT-C=h\cdot tan(76^o)-h\cdot tan(69^o)=600feet\\ h\cdot (tan(76^o)- tan(69^o))=600feet\)
\(h=\frac{600ft}{tan(76^o)-tan(69^o)}\)
\(h\approx 426.8\ ft\)
\( Pierre's\ line\ of\ sight\ above\ the\ Ground\ is\ 426.8\ feet\ high.\)
!