Answer:
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°
