The length of the radius of a sphere, in centimeters, is represented by the expression 5k⁴. The surface area of the sphere, in square inches, is 4π(5k⁴)². Which simplified expression represents the surface area of the sphere?

Select one:
A. 50πk6
B. 100πk6
C. 100πk8
D. 125πk8

D

Step-by-step explanation:

We see that the distance from the boat to the lighthouse is 120 metres, which means that the horizontal side of the triangle is 120.

We also know that the angle of elevation, x, is 40°. We want to find the height of the lighthouse, which is the vertical side of the triangle.

Since we are solving a trigonometry problem involving the two legs, we know that we will be using tangent, which is opposite / adjacent, as opposed to cosine, which is adjacent / hypotenuse. So, eliminate the first two choices.

As mentioned above, tangent is opposite / adjacent, where "opposite" is the side opposite the angle and "adjacent" is the side right next to the angle that is not the hypotenuse.

Here, the "opposite" side is the height of the lighthouse, which we want to find: y. The "adjacent" side is the distance from the boat to the lighthouse, which is given as 120 metres. The angle is 40°. We can then write:

tan(40°) = opposite / adjacent = y / 120

The answer is thus D.

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