In Exercises 39–40, find h to the nearest tenth.
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Verified step by step guidance

1. Identify the right triangle PQR where PQ is the height h, and angle PQR is 90 degrees.
2. Note that angle SRP is 59 degrees and angle PSR is 38 degrees, with SR = 288 units.
3. Use the fact that the sum of angles in triangle PSR is 180 degrees to find angle PRS: \(180^\circ - 38^\circ - 59^\circ = 83^\circ\).
4. Apply the Law of Sines in triangle PSR to find the length of PR: \(\frac{PR}{\sin 38^\circ} = \frac{288}{\sin 83^\circ}\), then solve for PR.
5. Use the right triangle PQR and angle 59 degrees to find height h by using \(h = PR \times \sin 59^\circ\).

Key Concepts

Right Triangle Trigonometry

Right triangle trigonometry involves using sine, cosine, and tangent ratios to relate the angles and sides of a right triangle. These ratios help find unknown side lengths or angles when some measurements are given, especially when a right angle is present.

Angle Sum Property of Triangles

The angle sum property states that the sum of the interior angles of any triangle is always 180°. This property helps determine unknown angles when two angles are known, which is essential for applying trigonometric ratios correctly.

Segment Addition and Geometric Decomposition

In problems involving multiple triangles sharing sides or points, segment addition allows breaking down a longer side into smaller parts. Decomposing the figure into right triangles helps apply trigonometric ratios step-by-step to find unknown lengths like height h.