Question

Find the height of the cliff. If necessary, round to the nearest hundredth yard.

Answer 1

We are given a diagram showing a slope, and a vertical height. We now have what represents a right angled triangle. The distance from the base of the cliff to the end of the slope is given as 24 yards. The slope itself is 37 yards. We shall now determine the height of the cliff (from ground to top) as indicated.

Note that we shall use the Pythagoras' theorem which is;

`c^2=a^2+b^2`

Where we have

`\begin{gathered} c=\text{hypotenuse (longest side)} \\ a,b=\text{other sides} \end{gathered}`

We can now substitute the given values/side lengths and we'll have;

`37^2=24^2+b^2`
`1369=576+b^2`

Subtract 576 from both sides;

`793=b^2`

Take the square root of both sides;

`\begin{gathered} \sqrt[]{793}=\sqrt[]{b^2} \\ 28.160255\ldots=b \end{gathered}`

Rounded to the nearest hundredth, the answer now becomes;

ANSWER:

`b=28.16yd`

The last option is the correct answer