Assume you are flying in an airplane and you see a mountain. You think, "How high is that mountain?" Given you know your flight altitude and can fly directly over the mountain...
Given | |
---|---|
flight altitude | 14,245 ft |
measurement distance | 4,100 ft |
Angle | 41° |
Angle | 36° |
1. Calculate the third angle of the triangle
θ = 180 - α - β
2. Using the length of the side opposite the angle θ and the
law of sines, calculate the length of the side opposite angle
L_{α} = (sin(α) * 4100) / sin(θ)
V_{distance} = sin(β) * L_{α}
4. Calculate the mountain's height by subtracting the vertical distance from the flight altitude
M_{height} = 14245 - V_{distance}
Create an interactive program. Let the user vary the input data.
These equations make no reality checks. With the right input data, you can be flying inside the mountain, or underground.
Create an interactive program to draw a diagram (triangle) like the one in project #1. Ask the user to enter:
Use graphics.py to draw the diagram (triangle). Click HERE for more information. (download, install, documentation, ...)
sin(α) sin(β) sin(δ) -------- = -------- = -------- A B C
Use the Law of Sines to solve oblique triangles. Any triangle that is not a right triangle is an oblique triangle.
Note: There are three possible oblique triangle problem situations: ASA (angle-side-angle), AAS (angle-angle-side), and SSA (side-side-angle).
Photogrammetry (Wikipedia)
Great Trigonometrical Survey (Wikipedia)
Greek Alphabet (Wikipedia)