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GEOMETRY TRIG

Plane\'s altitude is 3,000 ft. For the pilot, the angle of depression of the base of contol tower is 15 degrees. What is the distance from pilot to base of tower? Choice answers are 3106, 11591, 11198, 4346. I tried
cos 75 = A/H;
,92 = 3000/H;
.92 H = 3000;
H = 3000/.92;
3261 ANS not listed. Where did I go wrong?

718 day(s) ago

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Answers (7)

sin 15 =3000/H
H=3000/sin 15
H = 3000/0.25882
= 11591 ft............................Ans

Posted 710 dy ago

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jayteacher 		The altitude of the plane is 3000 ft. and the angle of depression is -15°. (The angle is negative since the measurement is of an angle of depression.) The equation sin (-15°) = (Opposite side of the angle -15°) / Hypotenuse. The distance of the plane to the base of the tower will be the hypotenuse.

Now cross multiply Hypotenuse and the sin (-15°). By the way the opposite side is -3000 because the displacement of the plane to the base of the tower is in the negative direction.

Hypotenuse = -3000 / sin (15°) = 11591 ft.

Posted 717 dy ago

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Plane\'s altitude is 3,000 ft. For the pilot, the angle of depression of the base of contol tower is 15 degrees. What is the distance from pilot to base of tower? Choice answers are 3106, 11591, 11198, 4346. I tried
cos 15 = A/H; {Because angle of depression is equal to angle of elevation}
0.965925826289= 3000/H;
H = 3000/0.965925826289
H = 3106..........................................Correct Answer


Posted 717 dy ago

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samzappala 		With this triangle alpha=15deg; beta=85deg; gamma=90deg. a/(sin alpha)=b/(sin beta)=c. So 3000/(sin15)=c=3000/.259=11,591 ft or 2.195 miles.

Posted 717 dy ago

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David 		I assume that you used a calculator, like me.
On my calculator, where I set the degree option for trigonometric functions:
cos(75 degrees)=0.2588, not 0.92
I think you didn't set the degree option on your calculator. Most advanced calculators have a default option for the radian unit of angle. When you buy it, the calculator is programmed to calculate the angles in radians, not degrees.


Posted 717 dy ago

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matherapist 		As math_fanatic said, check your evaluation of the cos of 75 deg or the sine of 15 deg. Your method is OK except for that

Posted 718 dy ago

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math_fanatic 		If I'm interpreting this correctly, you've got a right triangle with one angle that is 15 degrees and an opposite side that is 3000 ft. So you need to find the hypotenuse of the triangle to find the distance to the control tower.

You can use sine (opposite/hypotenuse) to solve this:

3000/H = sin(15)

3000/H = 0.25882

solve for H:

H = 3000/.25882 = 11591

I'm not sure where you went wrong. Cosine should have worked too with an angle of 75. You get the same answer:

cos 75 = 3000/H
.25882 = 3000/H
H = 3000/.25882 = 11591

Maybe you should check to make sure your calculator is operating in degrees. You should not have gotten .92 for cos 75.

Posted 718 dy ago

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