To approach the runway, a pilot of a small plane must begin a 10 degrees descent starting from a height of 1983 feet above the ground. to the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?

2.2 miles

The mnemonic SOH CAH TOA reminds you that

... Sin = Opposite/Hypotenuse

We are given an angle (10°) and its opposite side length (1983 ft), and we are asked to find the hypotenuse (the straight-line distance from the plane to the runway).

... sin(10°) = (1983 ft)/distance

Multiplying by distance and dividing by sin(10°), we have ...

... distance = (1983 ft)/sin(10°) ≈ 11419.6 ft

We want to express this in miles, so we have ...

... 11419.6 ft = (m mi)×(5280 ft/mi)

... (11419.6 ft)/(5280 ft/mi) = m mi ≈ 2.163 mi

Rounding to tenths, the distance is ...

2.2 miles

Comment on the question

The distance from the plane to the airport is different than the horizontal distance from the airport at which the descent must start. The latter distance is the "adjacent" leg of the triangle, so must be found using the tangent function. Rounded to tenths, it is 2.1 miles.

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.