Sadie the dog is sitting on the roof of his doghouse, 4.5 ft off the ground. He is watching a cat that is 16 ft away from the ba
se of the doghouse. What is the angle of depression from the roof of the doghouse to the cat? Round to the nearest hundredth. I watched the lesson but it all just went over my head, can someone simplify the explanation of how these problems work?
1 answer:
In word problems on topics of trigonometry, the terms of angle of depression and angle of elevation are very common. The angle of depression is used when the observer is above the point of reference. The angle made from the observer to the object is the angle of depression. To understand more clearly, refer to the attached picture.
Suppose the dog is on the top vertex of the triangle while the cat is the rightmost corner of the triangle. The angle denoted as x° is the angle of depression. To determine this, we use the tangent function. The tangent of an angle is the ratio of its opposite side to its adjacent side.
tanx° = 16/4.5
x = 74.29°
Suppose the dog is on the top vertex of the triangle while the cat is the rightmost corner of the triangle. The angle denoted as x° is the angle of depression. To determine this, we use the tangent function. The tangent of an angle is the ratio of its opposite side to its adjacent side.
tanx° = 16/4.5
x = 74.29°
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We know:
Length of the sides of the triangle
We want to know:
Length of the hypotenuse
Using the Pythagorean theorem we have:
Rewriting the expression we have:
Then, the distance that he would have saved if he travels directly is:
Answer:
he would have saved:
1.8 miles
We know:
Length of the sides of the triangle
We want to know:
Length of the hypotenuse
Using the Pythagorean theorem we have:
Rewriting the expression we have:
Then, the distance that he would have saved if he travels directly is:
Answer:
he would have saved:
1.8 miles