A 63 foot long cable is anchored in the ground and attached to the top of a light pole at an angle of
elevation of 52 degrees. Find the height of the light pole
to the nearest foot.

The height of the light pole to the nearest foot is approximately 50 feet

Step-by-step explanation:

The parameters given in the question are;

The length of the cable = 63 feet

The angle of elevation of the cable to the top of the light pole = 52°

With the assumption that the light pole is perpendicular to the ground, the figure formed by the light pole, the distance of the of the cable from the base of the light pole and the length of the cable form a right triangle

The question can be answered by using trigonometric relations for the sine of the given angle as follows;

The opposite leg length of the formed right triangle = The height of the light pole

The hypotenuse length = The length of the cable = 63 feet

The angle, θ = The angle of elevation = 52°

Plugging in the values, gives;

∴ The height of the light pole = 63 feet × sin(52°) ≈ 49.645 feet

The height of the light pole to the nearest foot ≈ 50 feet.

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !