Question

Can you please help me with my exit ticket assessment

Answer 1

Approximately, the distance between the cliff and the boat is 64 feet

Here, we want to calculate the distance between Caterina's boat and the cliff

From the question, we can have two similar right-angled triangles

The first is the one that the Cliff makes with the boat while the second is the one Caterina makes with the boat while standing on the cliff

The first smaller one measures;

35 ft by x ft (where x is the distance from the cliff to the boat

The second smaller one, measures

(35 + 5.5) by (10+x) feet

That would be 40.5 by (10+x) feet

If two traingles are similar, the ratio of their sides are equal

Thus, mathematically;

`\begin{gathered} (35)/(x)\text{ = }(40.5)/(10+x) \\ \\ 35(10+x)\text{ = 40.5(x)} \\ \\ 350\text{ + 35x = 40.5x} \\ \\ 350\text{ = 40.5x-35x} \\ \\ 5.5x\text{ = 350} \\ \\ x\text{ = }(350)/(5.5) \\ \\ x\text{ = 63.64} \end{gathered}`