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LUCKY_DIMON [66]
4 years ago
13

A hot-air balloon is floating above a straight road. To calculate their height above the ground, the balloonists simultaneously

measure the angle of depression to two consecutive mileposts on the road on the same side of the balloon. The angles of depression are found to be 24∘ and 27∘.
Physics
1 answer:
docker41 [41]4 years ago
6 0

Answer:

Height of the balloon is 6.923 miles or 11141.46m

Explanation:

We form two triangles with a common vertex so the relation of the angles is and the position both are measuring

tan(27)=\frac{Op}{Ad}\\Op1=Ad*Tan(27)\\Op1=Ad*0.595

The second triangle have the mileposts on the road  that is a mile more so:

tan(24)=\frac{Op}{Ad+1mile} \\Op=tan(24)*(Ad+1mile)\\Op=0.445*(Ad+1mile)

Op=0.445*Ad+0.445

Now resolve the both equation to know the opposite side that is the height of the hot air balloon

Op*0.595=Op*0.4452+0.4452\\Op*(0.595-0.4452)=0.4452\\Op*0.0643=0.4452\\Op=\frac{0.4452}{0.0643}

Op=6.923 mile

Height=6.923miles

Leigth can be find also

Ad=tan(27)*6.923\\Ad=3.52 miles

The measure can be express in meters so

6.923miles*\frac{1.60934km}{1mile}=11.4146km\\11.14146km*\frac{1000m}{1km}=11141.4608 m

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