A particular airport has beacons on the ground 5 km out from the start of each runway. An airplane is directly over this beacon and is at an angle of elevation from the runway of 9°. Calculate the direct line distance from the airplane to the start of the runway

The direct distance from the plane to the start of the runway is approximately 5.0623 km

Step-by-step explanation:

The locations of the beacons on the runway, x = 5 km from the start of each runway

The angle of elevation of the airplane from the runway, θ = 9°

Let 'R' represent the direct distance from the plane to the start of the runway

The horizontal distance from the start of the runway to the beacon, 'x', the distance from the plane to the start of the runway, 'R', and the vertical height of the plane, 'h' form a right triangle with rides x, R, and h

By trigonometric ratios, we have;

Therefore, we have;

From which we have;

The direct distance from the plane to the start of the runway, R ≈ 5.0623 km

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.