Question

a plane flies 1.7 hours at 110 mph on a bearing of 10°. it then turns and flies 9.6 hours at the same speed on a bearing of 100°. how far is the plane from its starting point? the plane is miles from its starting point. (round to the nearest whole number.)

Explanation:

Step1: Calculate the two - side lengths of the triangle

The distance formula is $d = vt$. For the first part of the flight, $v = 110$ mph and $t=1.7$ hours, so $a = 110\times1.7=187$ miles. For the second part of the flight, $v = 110$ mph and $t = 9.6$ hours, so $b=110\times9.6 = 1056$ miles. The included - angle $\theta$ between the two paths is $100^{\circ}-10^{\circ}=90^{\circ}$.

Step2: Use the Pythagorean theorem

In a right - triangle with side lengths $a$ and $b$ and hypotenuse $c$, the Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$. Substitute $a = 187$ and $b = 1056$ into the formula: $c=\sqrt{187^{2}+1056^{2}}=\sqrt{34969 + 1115136}=\sqrt{1150105}\approx1072$.

Answer:

1072