Math  /  Trigonometry

QuestionAn aircraft is climbing at a 30 degree angle to the horizontal. How fast is the aircraft gaining altitude if its speed is 500mi/hr500 \mathrm{mi} / \mathrm{hr} ? Express your answer as mi/hr\mathrm{mi} / \mathrm{hr} and round it into the nearest whole number. Input only the numerical value of the answer without the unit.

Studdy Solution
Calculate the sine of 30 30^\circ , which is 0.5 0.5 , and then find the vertical speed:
Vertical Speed=500mi/hr×0.5 \text{Vertical Speed} = 500 \, \text{mi/hr} \times 0.5 =250mi/hr = 250 \, \text{mi/hr}
Round the result to the nearest whole number (though it is already a whole number).
The aircraft is gaining altitude at a speed of:
250 \boxed{250}

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