Find the range of the function.
1 answer:
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(a) See the attached sketch. The jet makes a right triangle with the ground with hypotenuse <em>y</em>. Since the angle of depression is 56°, and the plane in which the jet is flying 300 m in the air is parallel with the ground, the angle of elevation in the right triangle is also 56°. Use the definition of sine to solve for <em>y</em>.
sin(56°) = (300 m)/<em>y</em> → <em>y</em> = (300 m)/sin(56°)
The uppermost angle in the blue triangle has measure equal to the difference between the two given angles of depression, 56° - 30° = 26°, and the rightmost angle is also 30° by the same reasoning as before. Then by the law of sines,
<em>x</em>/sin(26°) = <em>y</em>/sin(30°) → <em>x</em> = sin(26°)/sin(30°) <em>y</em> ≈ 317.2627 m
(b) No, the field is not long enough.
