Question

A flagpole AB, of height of 5.8 m, stands on top of a wall BC. ABC forms a straight line. The wall leans slightly so that it makes an angle of 96° with the horizontal grund CD. The angle of elevation of the top of the wall, B, from the point D is 38° Given that BC is 27.3 m, clculate AD.

Answer 1

Answer:

The length AD is approximately 48.3 m

Step-by-step explanation:

Notice that in triangle CBD, angle B can be found by subtracting $96^o$ and $38^o$ from $180^o$ (addition of all internal angles of a triangle must be $180^o$):

$180^o-96^o-38^o=46^o$

So we complete the value in the attached image

We go now into finding the length of the bottom side CD in the triangle CBD, by using the law of sines in that triangle:

$\frac{CD}{sin(46^o)} =\frac{27.3}{sin(38^o)} \\CD=\frac{27.3\,*\,sin(46^o)}{sin(38^o)} \\CD=31.9\,\,m$

Now we use this value in the law of cosines for the larger triangle ADC, since we know two sides and the angle in between:

$AD^2=AC^2+CD^2-2\,AC * CD * cos (96^o)\\AD^2=(5.8+27.3)^2+31.9^2-2*33.1*31.9*cos(98^o)\\AD^2=2334\\AD=48.3 \,\,m$