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She stood in front of the tree and started backing until she could see the top edge of the building from above the tree top.She marked her place and measured it from the tree. Knowing that the tree height is 2.8m and Trisha’s eyes height is 1.6m, help Trisha to do the math and calculate the building height.$\frac = \frac = \frac = \frac \Rightarrow 2.8 \times AC = 1.6 \times (5 AC) = 8 1.6 \times AC$ $(2.8 - 1.6) \times AC = 8 \Rightarrow AC = \frac = 6.67$ We can then use the similarity between triangles ΔACB and ΔAFG or between the triangles ΔADE and ΔAFG.
The ratio of the length of two sides of one triangle to the corresponding sides in the other triangle is the same and the angles between these sides are equal i.e.: $\frac=\frac$ and $\angle A_1 = \angle A_2$ or $\frac=\frac$ and $\angle B_1 = \angle B_2$ or $\frac=\frac$ and $\angle C_1 = \angle C_2$ Be careful not to mix similar triangles with identical triangle.
Identical triangles are those having the same corresponding sides’ lengths.
The road map can be geometrically expressed as shown by the figure below.
You may notice that the two triangles ΔABC and ΔCDE are similar and therefore: $\frac = \frac = \frac$ From the problem description, we have: AB = 15km, AC = 13.13km, CD = 4.41km and DE = 5km From the above, we can calculate the following lengths: $BC = \frac = \frac = 13.23km$ $CE = \frac = \frac = 4.38km$ In order for Steve to reach his friend’s house, he may follow any of the following routes: A - Trisha wants to measure the height of a building but she does not have the tools to do so.
First, let us denote each intersection point by a letter as shown in Red on the figure above.DE and they have the same apex angle C.It appears that one triangle is a scaled version of the other. AB