Question

Using his telescope, Tory watches a cheetah as it sits on the top of a cliff. The telescope is positioned so that the line of sight to the cheetah forms a 33° angle of elevation. The telescope sits 2.4 m above the ground and the base of the telescope is 193 m from the base of the cliff. To the nearest tenth of a meter, how high above the ground is the cheetah? If the answer does not have a tenths place then include a zero so that it does.

Answer 1

Given:

Tory watches a cheetah as it sits on the top of a cliff.

The line of sight to the cheetah forms a 33° angle of elevation.

The telescope sits 2.4 m above the ground.

The base of the telescope is 193 m from the base of the cliff.



Required:

We need to ind the height of hthe cliff.

Step-by-step explanation:

The Height of the cliff is BC.

We need to find the measure of BC.

We know that AD=AB=193m, and T=BD=2.3m.

Let DC=x m.

Consider the tan fomula.

`tan\theta=\frac{Opposite\text{ side}}{Adjacent\text{ side}}`

Substitute opposite side= DC=x and adjacent side = AD=193m in the formula.

`tan33^o=(x)/(193)`

`x=193* tan33^o`
`x=125.3m`
`\text{We know that }BC=BD+DC`

Substitute BD =2.4 m and DC=125.3 m in the equation.

`BC=2.4+125.3`
`BC=127.7m`

Fial answer:

The cheetah sits on the top of a cliff from 127.7m of the ground.