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Aleks [24]
3 years ago
12

A right triangle has base b = 100 plusminus 1 ft and adjacent angle theta = 30 degree plusminus 0.5 degree. Calculate the height

h and its uncertainty.
Physics
1 answer:
aivan3 [116]3 years ago
4 0

Answer:

The height h of this right triangle is 57.74±1.74ft.

Explanation:

Knowing that this is a right triangle, if one of the angles adjacent to the base, θ is 30º, the other angle is 90º. Therefore we can calculate the height h can be calculated with the tangent:

tan(\theta)=\frac{h}{b}\leftrightarrow h=tan(\theta)b=tan(30^\circ)100ft=57.74ft

For the uncertainty we use the  partial derivatives:

\Delta h=|\frac{dh}{db}|\Delta b+ |\frac{dh}{d\theta}|\Delta \theta\\\Delta h=|tan(\theta)|\Delta b+ |\frac{b}{cos^2(\theta)}|\Delta \theta

We have to be careful to use Δθ in radians:

\Delta h=|tan(30^\circ)|1ft+ |\frac{100ft}{cos^2(30^\circ)}|\frac{0.5^\circ2\pi}{360^\circ}=1.74ft

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