A bird is flying at an altitude of 400 feet and descending to its nest located in a tree 20 feet above the ground. The angle from the nest to the bird is 24 degrees. Approximately how far is the bird from the nest.

Question

Mathematics

Francisco Dorsey

26 March, 07:29

A bird is flying at an altitude of 400 feet and descending to its nest located in a tree 20 feet above the ground. The angle from the nest to the bird is 24 degrees. Approximately how far is the bird from the nest.

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Brayden Thompson · Answer 1

936m

Step-by-step explanation:

What we have here is a rght triangle, where one leg is the hight between the nest and the bird (400 - 20 = 380) and the other is the distance between the bird and the nest linearly from the ground (name it X). The hypotenuse is the distance the bird will fly (name it H).

Is not clear if we need to find X or H so we will find both.

First, to find H we use the trigonometric formula:

Sin (24) = leg opposed / hypotenuse

Sin (24) is 0.406 aprox

So,

0.406 = 380/h - > h = 380/0.406 = 936 (aprox)

Then we find X, the adjacent leg to 24° using the formula:

Cos (24) = X / hypotenuse

Cos (24) is approximately 0.91

So:

0.91 = X / 936 - > X=0.91*936 = 852 (aprox)

So, the distance ir 936 ir 852, depending on what you need. The statement is not very clear (however I guess it is 936 as is the distance the bird Weill fly)