An observer at point 0 sees airplane P directly over airport a. The observer measures the angle of the plane at 40.5. Find m<P
you have a right triangle. The two acute angles add to 90 degrees.
To find the measure of angle P, we need to know one more measurement. Specifically, we need to know the distance between the observer's position (point 0) and the airplane at that moment.
Without that information, it is not possible to determine the measure of angle P accurately. However, if we assume that the distance between the observer and the airplane is constant, we can use trigonometry to estimate the measure of angle P.
Let's assume the distance between the observer (point 0) and the airplane is d. Since the angle of elevation from the observer's position is given as 40.5°, we can set up a right triangle as follows:
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P /_______| O (observer)
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A (airport)
In this triangle, angle P is the angle of elevation, angle O is a 90° angle (since it's a right triangle), and angle A is the complementary angle to angle P.
Using trigonometry, we can write the following equation:
tan(angle P) = opposite/adjacent
tan(angle P) = A/O
tan(40.5°) = A/d
Now, assuming we know the value of d (the distance between the observer and the airplane), we can solve for A, the opposite side:
A = d * tan(40.5°)
However, without the value of d, we cannot determine the exact measure of angle P.