Karla is riding vertically in a hot air balloon, directly over a point P on the ground. Karla spots a parked car on the ground at an angle of depression of 30 degrees. The balloon rises 50 meters. Now the angle of depression to the car is 35 degrees. How far is the car from point P?
Answers
Step-by-step explanation:
Oct 26, 2012
We form 2 similar rt. triangles:
Triangle #1.
X = Hor. side = dist. from P to the car.
Yi = Ver. side.
A = 30o.
Triangle #2.
X = Hor. side = Dist. from P to the car.
Y2 = Y1+50 = Ver. side.
A = 35o.
Use aw of Sines.
sin30/Y1 = sin35/(Y1+50).
Cross multiply:
(Y1+50)sin30 = Y1*sin35
Y1/2+25 = 0.574Y1
Multiply both sides by 2:
Y1+50 = 1.148Y1
1.148Y1-Y1 = 50
0.148Y1 = 50
Y1 = 337.8 m.
tan30 = Y1/X = 337.8/X
X = 337.8/tan30 = 585 m.
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Answer:
Step-by-step explanation:X = Hor. side = dist. from P to the car.
Yi = Ver. side.
A = 30o.
Triangle #2.
X = Hor. side = Dist. from P to the car.
Y2 = Y1+50 = Ver. side.
A = 35o.
Use aw of Sines.
sin30/Y1 = sin35/(Y1+50).
Cross multiply:
(Y1+50)sin30 = Y1*sin35
Y1/2+25 = 0.574Y1
Multiply both sides by 2:
Y1+50 = 1.148Y1
1.148Y1-Y1 = 50
0.148Y1 = 50
Y1 = 337.8 m.
tan30 = Y1/X = 337.8/X
X = 337.8/tan30 = 585 m.