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Trigonometry question on finding an angle?
Looking at the image (please ignore the irrelevant shapes this is from a physics problem) how do we find θ2 if we know θ1 and d. At first I thought θ2 = θ1-angle who has d/1 as its tangent but it turned out negative when θ1 was 10 degrees and d was 6.6.
I forgot to mention the blue dashed line is at right angles to the small red line representing the diameter of the circle.
Oh god I just realized I'm the most stupid person ever and d = 6.6 CM not meters that's why it's all wrong
1 Answer
- Jeff AaronLv 75 years ago
It looks like there's a right-angled triangle with d as the top leg, 1m long on the left leg, and the hypotenuse is in red. If so, let's call x the bottom angle in that triangle, so we have:
tan(x) = d/1
x = arctan(d)
If d = 6.6, then x =~ 81.384351815835887719627972645329 degrees
Assuming the dashed blue line is straight and passes through the bottom vertex of that triangle, then we have:
x + Theta2 = Theta1
Theta2 = Theta1 - x
Theta2 =~ 10 - 81.384351815835887719627972645329
You're right, this is impossible, as Theta2 can't be less than Theta1.
With those numbers, the blue dashed line should pass THROUGH the triangle!
