12.2 Basic trigonometry  (Page 4/7)

To find the height of the tower, all we have to do is find the length of $CD$ and $DE$ . We see that $▵BDE$ and $▵BDC$ are both right-angled triangles. For each of the triangles, we have an angle and we have the length $AD$ . Thus we can calculate the sides of the triangles.

We are given that the length $AC$ is 100m. $CABD$ is a rectangle so $BD=AC=100\mathrm{m}$ .

Use your calculator to find that $tan{34}^{\circ }=0,6745$ . Using this, we find that $CD=67,45$ m

We have that the height of the tower $CE=CD+DE=67,45\mathrm{m}+188,07\mathrm{m}=255.5\mathrm{m}$ .

We already know the distance between Cape Town and $A$ in blocks from the given map (it is 5 blocks). Thus if we work out how many kilometers this same distance is, we can calculate how many kilometers each block represents, and thus we have the scale of the map.

Let us denote Cape Town with $C$ and Pretoria with $P$ . We can see that triangle $APC$ is a right-angled triangle. Furthermore, we see that the distance $AC$ and distance $AP$ are both 5 blocks. Thus it is an isoceles triangle, and so $A\widehat{C}P=A\widehat{P}C={45}^{\circ }$ .

To work out the scale, we see that

We see that the triangle $ABC$ is a right-angled triangle. As we have one side and an angle of this triangle, we can calculate $AC$ . The height of the wall is then the height of the garage minus $AC$ .

If $BC$ =5m, and angle $A\widehat{B}C=5^{\circ }$ , then

Thus we have that the height of the wall $BD=4\mathrm{m}-0.4358\mathrm{m}=3.56\mathrm{m}$ .