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1 math question help

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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

Feb 25, 2020

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How far above the ground is Pierre's line of sight?

Hello Guest!

$$C=h\cdot tan(90-21)\\ DT=h\cdot tan(90-14)\\ DT-C=h\cdot tan(76^o)-h\cdot tan(69^o)=600feet\\ h\cdot (tan(76^o)- tan(69^o))=600feet$$

$$h=\frac{600ft}{tan(76^o)-tan(69^o)}$$

$$h\approx 426.8\ ft$$

$$Pierre's\ line\ of\ sight\ above\ the\ Ground\ is\ 426.8\ feet\ high.$$

!

Feb 25, 2020