Two points, A and B, are 526 meters apart on a level stretch of road leading to a hill. The angle of elevation of the hilltop from A is 26deg30mins, and the angle of elevation from B is 36deg40mins. How high is the hill?
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height=793.561
To find the height of the hill, we can use the trigonometric concept of tangent.
Let's denote the height of the hill as h.
From point A, the angle of elevation to the hilltop is 26 degrees 30 minutes. We can use the tangent function:
tan(26°30') = h / AB
tan(26°30') = h / 526
We can do the same for point B:
tan(36°40') = h / AB
tan(36°40') = h / 526
Now, we have two equations:
tan(26°30') = h / 526 [Equation 1]
tan(36°40') = h / 526 [Equation 2]
To solve for h, we can solve these two equations simultaneously.
First, let's calculate the tangent of each angle:
tan(26°30') ≈ 0.4938
tan(36°40') ≈ 0.7559
Now, we can rewrite the equations using these values:
0.4938 = h / 526 [Equation 1]
0.7559 = h / 526 [Equation 2]
To solve for h, we can multiply both sides of each equation by 526:
0.4938 * 526 = h [Equation 1]
0.7559 * 526 = h [Equation 2]
This gives us:
h ≈ 259.6428 [Equation 1, rounded to the nearest decimal]
h ≈ 397.6234 [Equation 2, rounded to the nearest decimal]
Since both equations give slightly different values, we can take the average of these values to get a more accurate result:
(h ≈ 259.6428 + 397.6234) / 2 ≈ 328.6331
Therefore, the height of the hill is approximately 328.63 meters.