Processing Math: Done

From Förberedande kurs i matematik 1

If we extend the line AB to a point D opposite C, we will get the right-angled triangle shown below, where the distance x between C and D is the desired distance.

The information in the exercise can be summarized by considering the two triangles ACD and BCD, and setting up relations for the tangents that the angles 30° and 45° gives rise to,

x=(10+y)tan30=(10+y)13		x=ytan45=y1

where y is the distance between B and D.

The second relation above gives that y=x and substituting this into the first relation gives

x=(10+x)13.

Multiplying both sides by 3  gives

3x=10+x

moving all the x-terms to the left-hand side gives

(3−1)x=10.

The answer is

x=103−1 m13.6 m.