Question

A trigonometry student stands 25 meters from a building and measures the angle of elevation to the top of the building as 30â°. how accurate does her angle measurement have to be if she wants her propagated percentage error in estimating the height of the building to be no more than 5%?

Answer 1

Using the slope concept, it is found that the angle measurement has to be within 1.2º of 30º.

What is a slope?

The slope is given by the vertical change divided by the horizontal change, and it's also the tangent of the angle of depression.

In this problem, considering the horizontal distance and the actual angle, the following equation is applied to find the actual height:

$\tan{30^\circ} = \frac{h}{25}$

$h = 25\tan{30^\circ}$

h = 14.43.

For an error of 5%, the bounds of h are as follows:

$h_{min} = 0.95 \times 14.43 = 13.71$

$h_{max} = 1.05 \times 14.43 = 15.15$

Hence, the angles will be given by:

$\tan^{\alpha} = \frac{13.71}{25}$

$\alpha = \tan^{-1}{\left(\frac{13.71}{25}\right)}$

$\alpha = 28.8$

$\tan^{\alpha} = \frac{15.15}{25}$

$\alpha = \tan^{-1}{\left(\frac{15.15}{25}\right)}$

$\alpha = 31.2$

Hence the angle measurement has to be within 1.2º of 30º.

More can be learned about the slope concept at brainly.com/question/18090623