From the hay loft door, Ted sees his dog on the ground. The angle of depression of the dog is 40º. Ted's eye level is 16 feet ab
ove the ground. How many feet must the dog walk to reach the open barn door directly below Ted (to the nearest foot)?
1 answer:
Answer: 19 feet
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the next trigonometric function.
Tan α = opposite side / adjacent side
Where α is the angle of depression of the dog, the opposite side (16) is Ted's eye level above the ground, and the adjacent side (x) is the distance between the dog and the barn door.
Replacing with the values given:
tan40 = 16/x
Solving for x
x =16/tan40
x= 19 ft
Feel free to ask for more if needed or if you did not understand something.
You might be interested in
Answer:
4:1 (I think)
Step-by-step explanation:
Let's write some equations first:
For both prices increasing by 20:
then we can use cross multiplication
2x+40=5y+100
For both prices decreasing by 5:
same here:
5y-25=x-5
Using substitution for 5y, we get: 5y=x+20
2x+40=5y+100
2x+40=x+20+100
x=80
plugging this in to the second equation:
5y-25=x-5
5y-25=80-5
5y-25=75
5y=100
y=20
therefore we get x:y=80:20
4:1