Atree casts a shadow that is 20 feet long. if the tree is 35 feet tall, what is the angle of elevation from the end of the shadow to the top of the tree? round to the nearest tenth

The angle of elevation is 60.3°

Step-by-step explanation:

* Lets revise the trigonometry functions

- In any right angle triangle:

# The side opposite to the right angle is called the hypotenuse

# The other two sides are called the legs of the right angle

* If the name of the triangle is ABC, where B is the right angle

∴ The hypotenuse is AC

∴ AB and BC are the legs of the right angle

- ∠A and ∠C are two acute angles

- For angle A

# sin(A) = opposite/hypotenuse

∵ The opposite to ∠A is BC

∵ The hypotenuse is AC

∴ sin(A) = BC/AC

# cos(A) = adjacent/hypotenuse

∵ The adjacent to ∠A is AB

∵ The hypotenuse is AC

∴ cos(A) = AB/AC  

# tan(A) = opposite/adjacent

∵ The opposite to ∠A is BC

∵ The adjacent to ∠A is AB

∴ tan(A) = BC/AB

* Now lets solve the problem

∵ The shadow of the tree is 20 feet long

- The shadow of the tree is on the ground

∵ The height of the tree is 35 feet tall

∴ The shadow of the tree and the height of the tree formed the legs of

  a right triangle

- The angle of elevation is opposite to the tree

∴ The shadow of the tree is the adjacent side of the angle of elevation

∴ The height of the tree is the opposite side of the angle of elevation

- let the name of the angle of elevation is Ф

∴ tan Ф = tree height/shadow length

∴ tan Ф = 35/20 = 7/4

∴ Ф = tan^-1(7/4) = 60.3°

* The angle of elevation is 60.3°

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step-by-step explanation: