Use trig ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Solve a structure problem with separate length and angle fields
Problem
A \(13\text{-}\text{ft}\) ladder reaches \(12~\text{ft}\) up a wall. First solve \(b^{2}+12^{2}=13^{2}\) for its base distance \(b\); then use a trigonometric ratio to calculate the ground angle \(θ\) to the nearest tenth of a degree.
This structure problem has two targets that call for two connected methods. We’ll identify the ladder as the hypotenuse, use the Pythagorean theorem for the positive base distance, form a trig ratio for the ground angle, and round the angle while preserving length units.
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