Question

Refer to the scenario below to answer the following questions: (a) Why are triangles RST and VUT similar? (b) What is the height of the tree?

Answer 1

The triangles are similar because they have the same internal angles. That is,

∠S ≅ ∠U

∠T ≅ ∠T

∠R ≅ ∠V

Given that they are similar, then their sides are in proportion, as follows:

`(SR)/(UV)=(RT)/(TV)`

Replacing with data and solving for x,

`\begin{gathered} \frac{1.7\text{ m}}{x\text{ m}}=\frac{1.2\text{ m}}{31.5\text{ m}} \\ 1.7\cdot31.5=1.2\cdot x \\ 53.55=1.2\cdot x \\ (53.55)/(1.2)=x \\ 44.625\text{ m =x} \end{gathered}`