Mathematics, 08.07.2019 05:20 parkbro3956
In traveling across flat land, you see a mountain directly in front of you. its angle of elevation (to the peak) is 3.5°. after you drive 15 miles closer to the mountain, the angle of elevation is 9° (see figure). approximate the height of the mountain. (round your answer to one decimal place.)
Answers: 1
![\bf tan(3.5^o)=\cfrac{y}{15+x}\implies 15+x=\cfrac{y}{tan(3.5^o)}\\\\\\ \boxed{x=\cfrac{y}{tan(3.5^o)}-15} \\\\\\ tan(9^o)=\cfrac{y}{x}\implies x\cdot tan(9^o)=y\\\\\\ \left[ \cfrac{y}{tan(3.5^o)}-15 \right]tan(9^o)=y \\\\\\ \left[ \cfrac{y-15tan(3.5^o)}{tan(3.5^o)} \right]tan(9^o)=y \\\\\\](/tpl/images/0064/4142/7e23e.png)
![\bf \cfrac{y\cdot tan(9^o)-15tan(3.5^o)tan(9^o)}{tan(3.5^o)}=y \\\\\\ y\cdot tan(9^o)-15tan(3.5^o)tan(9^o)=y\cdot tan(3.5^o) \\\\\\ ytan(9^o)-ytan(3.5^o)=15tan(3.5^o)tan(9^o) \\\\\\ \stackrel{common~factor}{y}[tan(9^o)-tan(3.5^o)]=15tan(3.5^o)tan(9^o) \\\\\\ y=\cfrac{15tan(3.5^o)tan(9^o)}{tan(9^o)-tan(3.5^o)}](/tpl/images/0064/4142/b0c42.png)
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In traveling across flat land, you see a mountain directly in front of you. its angle of elevation (...
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