Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 year ago

# How do I do this trigonometry question?

In the sport of air racing, small planes have to travel between two large towers (or pylons). The gap between a pair of pylons is smaller than the wing-span of the plane, so the plane has to go

through on an angle with one wing ‘above’ the other. The wing-span of a competition airplane is 8 metres.

a. Determine the angle, correct to 1 decimal place, that the plane has to tilt if the gap between pylons is 7 metres

b. Because the plane has rolled away from the horizontal as it travels between the pylons it loses speed. If the plane’s speed is below 96 km/h it will stall and possibly crash. For each degree of ‘tilt’ the speed of the plane is reduced by 0.98 km/h. What is the minimum speed the plane must go through each of the pylons in part a? Write your answer correct to 2 decimal places.

Relevance
• Anonymous
1 year ago

That airplane race is just too dangerous!

• Mike G
Lv 7
1 year ago

a) A = 'Tilt'' Angle

cos A = 7/8

A = 28.955°

b) Vmin = Minimum Safe Pylon Speed

Vmin - 0.98A = 96

Vmin = 96+0.98*28.955 = 124.3759

• 1 year ago

(a) Hypotenuse = 8 meters, Horizontal leg = 7 meters;

the angle is arccos(7/8) = 28.955 degrees, round to 29.0 deg.

(b) This question is poorly phrased. The plane must go through the pylons at 96 km/h. But I think what they want is the speed the plane must have just BEFORE it rolls through the 29-degree angle, in order to maintain 96 km/h when it has tilted.

96 km/h + (0.98 km/h)*29 = 124.42 km/h.