A 25 foot guy wire is attached to a sapling. The distance from the end of the wire to the base is 23 feet. What is the angle of elevation of the guide wire

23.1°

Explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are scalene, acute, obtuse, isosceles, equilateral and right angled triangle.

A right angled triangle is a triangle with one angle equal to 90 degrees. The longest side of a right angled triangle is known as the hypotenuse. Trigonometric identities is used to show the relationship between the angles and sides of a right angled triangle, i.e.:

sinθ = opposite/hypotenuse; cosθ = adjacent / hypotenuse; tanθ = opposite / adjacent

From the question,  a right angled triangle is formed. The hypotenuse = length of guide wire = 25 ft, height of triangle = height of sapling, base of triangle = distance from the end of the wire to the base = 23 ft.

Let θ be the angle of elevation. Hence:

cosθ = 23 ft / 25 ft

cosθ = 0.92

θ = cos⁻¹(0.92) = 23.1°