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Benjamin has a ladder that is 15 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 13.8 ft above the ground. What is the angle, rounded to the nearest tenth, that the ladder makes with the ground? Show your work and draw a diagram to support your answer.

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raphealnwobi

The ladder makes an angle of 66.9° with the ground.

A right angled triangle is a triangle (has three sides and three angles) in which one of the angles measure 90°.

Trigonometric ratios is used to show the relationship between the sides of the right angled triangle and its angles.

The ladder is 15 ft long and the wall is 13.8 ft long. Let θ represent the angle that the ladder makes with the ground. Hence:

sinθ = 13.8/15

sinθ = 0.92

θ = 66.9°

Therefore the ladder makes an angle of 66.9° with the ground.

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