Foundations of PreCalculus Chapter 5: The Trigonometric Functions Section 5.4-­‐ Applying Trigonometric Functions SWBAT: use trigonometry to find the measures of the sides of right triangles. Common Core: F.TF.2 Trig functions can be used to solve problems involving right triangles. The most common functions used are sine, cosine, and tangent. Example 1: a) If 𝑃 = 35° and r = 14, find q. b) If 𝐽 = 50° and g = 10, find r. Example 2: The circus has arrived and the roustabouts must put up the main tent in a field near town. A tab is located on the side of the tent 40 feet above the ground. A rope is tied to the tent at this point and then the rope is placed around a stake on the ground. a) If the angle that the rope makes with the level ground in 52° 15′, how long is the rope? b) What is the distance between the bottom of the tent and the stake? Foundations of PreCalculus Chapter 5: The Trigonometric Functions Example 2: The chair lift at a ski resort rises at an angle of 20.75° and attains a vertical height of 1200 feet. a) How far does the chair lift travel up the side of the mountain? b) A film crew is a helicopter records an overhead view of a skier’s downhill run from where she gets off the chair lift at the top of the mountain to where she gets back on the chair lift for her next run. If the helicopter follows a level flight path, what is the length of that path? Example 3: A regular pentagon is inscribed in a circle with diameter 8.34cm. The apothem of a regular polygon is the measure of the segment from the center of the polygon to the midpoint of one of its sides. Find the length of the apothem of the pentagon. Foundations of PreCalculus Chapter 5: The Trigonometric Functions A regular hexagon is inscribed in a circle with diameter 26.6cm. The apothem of a regular polygon is the measure of the segment from the center of the polygon to the midpoint of one of its sides. Find the length of the apothem of the hexagon. An ____________________________________________________ is the angle between a horizontal line and the line of sight from an observer to an object at a higher level. An ____________________________________________________ is the angle between the horizontal line and the line of sight from the observer to an object at a lower level. The angle of elevation and depression are equal in measure because they are _________________________________________________. Foundations of PreCalculus Chapter 5: The Trigonometric Functions Example 4: On May 18, 1980, Mount Saint Helens, erupted with such a force that the top of the mountain was blown off. To determine the new height at the summit of Mount Saint Helens, a surveyor measured the angle of elevation to the top of the volcano to be 37° 46′. The surveyor then moved 100 feet closer to the volcano and measured the angle of elevation to be 40° 30′. Determine the new height of Mount Saint Helens. Example 5: An observer in the top of a lighthouse determines that the angles of depression to two sailboats that lie directly in line with the lighthouse are 3.5° 𝑎𝑛𝑑 5.75°. If the observer is 125 feet above sea level, find the distance between the boats. Homework: Pgs. 302 – 303 #’s 10 – 23, and 25 – 27