A 10 foot tree create a shadow that is 15 feet long. Find the angle of elevation of the sun

The angle of elevation of the sun is 33.7⁰

Step-by-step explanation:

let the height of the tree, T = 10 foot

length of the shadow created by the tree, B = 15 feet long

Height of the tree and the shadow of the tree forms a right angle triangle with the remaining side that joins the two which is known as hypotenuse.

Let the remaining side, hypotenuse, L = ?

Apply Pythagoras theorem;

L ² = T² + B²

L ² = 10² + 15²

L ² = 325

L = √325

L = 18.03 ft

The angle of elevation of the sun, is the angle facing the height of the tree with the length of the shadow of the tree as adjacent of the triangle.

Let the angle of elevation = θ

tan θ = opp / adj

tan θ  = 10 / 15

tan θ  = 0.66667

θ = tan ⁻¹ (0.66667)

θ = 33.7⁰

Therefore, the angle of elevation of the sun is 33.7⁰

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