From a hand glider approaching a 6000 foot clearing the angles of depression of the opposite ends of the field measure 24 degrees and 30 degrees. how far is the hang glider from the nearer end of the field?
Math - drwls, Saturday, May 17, 2008 at 11:40pm
The third angle of the triangle formed by the hang glider and the two edges of the field is 180 - 24 - 30 = 126 degrees. This is the angle subtended by the field. The side opposite that subtended angle has a length of 6000 ft (the clearing length). Use the law of sines for the other two triangle sides. The side opposite the 24 dsegree corner will be the distance to the nearest edge.
Tareena:
Suppose
A=30
B=24
C=126
sin A= sin30 x 6000/sin 126=3708
sin B= sin24 x 6000/sin 126=6148
My mistake. The closest edge has the largest angle of depression.
Your method is correct, but you are solving for sides a and b, not the angles A and B .
a = 3708 m is the answer.
I think the angles of the triangle are:
24
180-30 = 150
180 - 24 - 150 = 30 - 24 = 6
so I think
sin 24 / x = sin 6/6000
x = 6000 (sin 24 /sin 6)
= 6000 (.407/.105) = 23,257
To find the distance of the hang glider from the nearer end of the field, we can use the Law of Sines.
First, let's label the angles:
A = 30 degrees
B = 24 degrees
C = 126 degrees
We know that the side opposite angle A (the distance to the nearest end of the field) can be found by:
sin A = (side opposite angle A) / (length of clearing)
Rearranging the equation, we have:
(side opposite angle A) = sin A * (length of clearing)
Now we substitute the values:
(side opposite angle A) = sin 30 * 6000
(side opposite angle A) = 0.5 * 6000
(side opposite angle A) = 3000
Therefore, the hang glider is 3000 feet away from the nearer end of the field.