Question

A hedgehog wishes to cross a road without being runover he observer the angle of elevation of a lamp post on the other side of the road to be 45degrees from the edge of the road and 30degrees from a point 10m back from the road how wide is the road

Answer 1

Answer:

13.6612

Step-by-step explanation:

I Given Complete Explanation In The Photo....

I Hope This Answer Will Help You....

Answer 2

Given:

Angle of elevation from the edge of the road to the lamp post = 45°

Angle of elevation from a point 10 m back of the road to the lamp post = 30°

To Find:

The width of the road

Solution

* See attached for a visual representation of the question

Define W and H:

Let the width of the road be W.

Let the height of the lamp post be H.

Find the height of the lamp post from point A:

$\tan \theta = \dfrac{\text{Opposite}}{\text{Adjacent}}$

$\tan (45) = \dfrac{\text{H}}{\text{W}}$

$H = W \tan(45)$

Find the height of the lamp post from point B:

$\tan \theta = \dfrac{\text{Opposite}}{\text{Adjacent}}$

$\tan (30) = \dfrac{\text{H}}{\text{W + 10}}$

$H = (W + 10) \tan(30)$

Solve W:

$W \tan(45) = (W + 10) \tan (30)$

$W \tan(45) = W \tan (30) + 10 \tan(30)$

$W \tan(45) - W \tan (30) = 10 \tan(30)$

$W (\tan(45) - \tan (30) )= 10 \tan(30)$

$W = \dfrac{10 \tan(30)}{\tan(45) - \tan(30)}$

$W = 13.66 \text { m}$

Answer: The Width of the road is 13.66 m