Atree casts a shadow that is 60 feet long, there is a 32degree angle of elevation from the tip of the shadow to the tree. how tall is the tree.

39.6 feet tall

Step-by-step explanation:

From what the problem says, we know that the shadow, the ground, and the tree make a triangle. We also know that the tip of the shadow has a 32° angle of elevation. So how do we use this information to find the height of the tree?

Through the use of trigonometric ratios, we'll be able to find the height of the tree. There are three trigonometric ratios which are shown below:

Sine∅ = (Opposite ÷ Hypotenuse)

Cosine∅ = (Adjacent ÷ Hypotenuse)

Tangent∅ = (Opposite ÷ Adjacent)

In the situation given to us, the hypotenuse of our triangle would be the diagonal from the top of the tree to the tip of the shadow. However, we are not given the measurement of the hypotenuse nor are we being asked to find the measurement.

The trigonometric ratio that we will need to use is tangent.

Tangent∅ = (Opposite ÷ Adjacent)

We already know that we need to find the tan(32°) but how can we tell what is the opposite and what is the adjacent? Well if you remember that the 32° angle is where the tip of the shadow is on the ground, then we know that the ground has to be the adjacent and the tree has to be the opposite giving us this equation:

tan(32°) = (x ÷ 60)

Solve for x.

(0.66) = (x ÷ 60)

x = 39.6 feet

~Hope this helps!~

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40