1) A television tower is 160 feet high and an observer is 120 feet from the base of the tower. Find, to the nearest degree, the angle of elevation of the top of the tower from the point of observation.

2) A vertical pole 22 meters tall casts a shadow 16 meters long on level ground. Find, to the nearest degree, the measure of the angle of elevation of the sun.
3) From the top of a cliff 90 feet high, the angle of depression of an object on the ground measures 40 degrees. Find, to the nearest hundredth, the distance from the object to the base of the cliff.

For each of them , make a sketch

In each case you will get a right-angled triangle
You MUST know the basic trig ratios in terms of
opposite, adjacent, and hypotenuse.
e.g. tanØ = opposite/adjacent

1) so we have tanØ = 160/120 = 4/3
Make sure your calculator is set to 'degrees'
( the D in your DRG button, mine shows DEG in small print at the top)
enter:
4
÷
3
=
2ndF
tan
=

you should get 53.130...
so to the nearest degree, the angle is 53

2) identical question

3) your text, notes, or your teacher should have explained the meaning of "angle of depression" and "angle of elevation"
try this one, let me know what you get.

WHAT IS MEDVIAL PIROD

To find the angle of elevation of the top of the tower from the point of observation, we can use trigonometry.

1) Let's label the height of the tower as "h" and the distance from the base of the tower to the observer as "d". We want to find the angle of elevation, which we'll call "θ".

Using the tangent function, we have:
tan(θ) = h/d

Substituting the given values, we have:
tan(θ) = 160/120

To find θ, we take the inverse tangent (or arc tangent) of both sides:
θ = arctan(160/120)

Using a calculator, we can find θ to be approximately 51.34 degrees (rounded to the nearest degree).

2) To find the measure of the angle of elevation of the sun, we can again use trigonometry.

Let's label the height of the pole as "h" and the length of the shadow cast by the pole as "s". We want to find the angle of elevation of the sun, which we'll call "θ".

Using the tangent function, we have:
tan(θ) = h/s

Substituting the given values, we have:
tan(θ) = 22/16

To find θ, we take the inverse tangent of both sides:
θ = arctan(22/16)

Using a calculator, we can find θ to be approximately 56.31 degrees (rounded to the nearest degree).

3) To find the distance from the object to the base of the cliff, we can use trigonometry again.

Let's label the height of the cliff as "h" and the angle of depression as "θ". We want to find the distance, which we'll call "d".

Using the tangent function, we have:
tan(θ) = h/d

Substituting the given values, we have:
tan(40 degrees) = 90/d

To find d, we rearrange the equation:
d = 90/tan(40 degrees)

Using a calculator, we can find d to be approximately 96.72 feet (rounded to the nearest hundredth).

1) To find the angle of elevation, we can use the inverse tangent function, also known as the arctan function. In this case, we want to find the angle (let's call it θ) that relates the height of the tower (opposite side) to the distance from the base of the tower to the observer (adjacent side).

Using the given information, the opposite side is 160 feet and the adjacent side is 120 feet. Therefore, we can use the equation:

tan(θ) = opposite / adjacent

tan(θ) = 160 / 120

Now, we can find the angle of elevation by taking the inverse tangent (arctan) of both sides:

θ = arctan(160 / 120)

Using a calculator or an online tool to find the arctan, we get:

θ ≈ 48.19 degrees

Therefore, the angle of elevation of the top of the tower from the point of observation is approximately 48.19 degrees.

2) To find the angle of elevation of the sun, we can use similar trigonometric principles. In this case, we have the height of the pole (opposite side) and the length of the shadow (adjacent side). Let's call the angle we are looking for θ.

Using the given information, the opposite side is 22 meters and the adjacent side is 16 meters. Therefore, we can use the equation:

tan(θ) = opposite / adjacent

tan(θ) = 22 / 16

Next, we can find the angle of elevation by taking the inverse tangent (arctan) of both sides:

θ = arctan(22 / 16)

Using a calculator or an online tool to find the arctan, we get:

θ ≈ 55.06 degrees

Therefore, the measure of the angle of elevation of the sun is approximately 55.06 degrees.

3) To find the distance from the object to the base of the cliff, we can use the tangent function. In this case, we have the height of the cliff (opposite side) and the angle of depression (adjacent side). Let's call the distance we are looking for x.

Using the given information, the opposite side is 90 feet and the angle of depression is 40 degrees. Therefore, we can use the equation:

tan(40 degrees) = opposite / adjacent

tan(40 degrees) = 90 / x

Next, we can rearrange the equation to solve for x:

x = 90 / tan(40 degrees)

Using a calculator or an online tool to find the tangent, we get:

x ≈ 90 / 0.839

x ≈ 107.22 feet

Therefore, the distance from the object to the base of the cliff is approximately 107.22 feet.