Applications of Right Triangles Section 1.5 Standard: MM2G2c

Applications of Right Triangles Section 1.5 Standard: MM2G2c Essential Question: How do trig ratios apply to real world applications?

Hints on solving trigonometry applications or problems: • If no diagram is given, draw one yourself. • Mark the right angles in the diagram. • Show the sizes of the other angles and the • lengths of any segments that are known • Mark the angles or sides you have to calculate.

Hints on solving trigonometry applications or problems-continued: • Consider whether you need to create right • triangles by drawing extra lines. For example, • divide an isosceles triangle into two congruent • right triangles. • Decide whether you will need the Pythagorean • Theorem, or a trig function: sine, cosine or • tangent. • Check that your answer is reasonable. The • hypotenuse is the longest side in a right triangle.

angle of depression angle of elevation Angle of Depression: the angle between the horizontal and the line of sight to an object below the horizontal. Angle of Elevation: the angle between the horizontal and the line of sight to an object above the horizontal. angle of depression = angle of elevation

(1). A forest ranger is on a fire lookout tower in a national forest. His observation position is 214.7 feet above the ground when he spots an illegal campfire. The angle of depression of the line of site to the campfire is 12°. a. The angle of depression is equal to the corresponding angle of elevation. Why? b. Assuming that the ground is level, how far is it from the base of the tower to the campfire?

(1a). The angle of depression is equal to the corresponding angle of elevation. Why? (1b). Assuming that the ground is level, how far is it from the base of the tower to the campfire? Alternate Interior Angles are Congruent 214.7 x The fire is 1,010.1 feet from the base of the tower.

(2). A ladder 5 m long, leaning against a vertical wall makes an angle of 65˚ with the ground. a) How high on the wall does the ladder reach? b) How far is the foot of the ladder from the wall? c) What angle does the ladder make with the wall? 5 m x The ladder reaches 4.5 m up the wall. 65o

(2). A ladder 5 m long, leaning against a vertical wall makes an angle of 65˚ with the ground. b) How far is the foot of the ladder from the wall? 5 m 65o The foot of the ladder is 2.1 m from the wall. y

(2). A ladder 5 m long, leaning against a vertical wall makes an angle of 65˚ with the ground. c) What angle does the ladder make with the wall? zo 5 m The ladder makes a 25o angle with the wall. 65o

(3). The ends of a hay trough for feeding livestock have the shape of congruent isosceles trapezoids as shown in the figure below. The trough is 18 inches deep, its base is 30 inches wide, and the sides make an angle of 118° with the base. How much wider is the opening across the top of the trough than the base? x 118o – 90o = 28o 18 28o 90o The opening across the top is 2(9.6) or 19.2 in. wider than the base.

Investigation 1: In your group, select one person as the recorder, one as the calculation expert, and one as the presenter. Work the problem assigned to your group on poster paper including a labeled diagram, equation with solution, and answer written in sentence form. The presenter will demonstrate your solution to the class.

(4). A guy wire is attached from the top of a tower to a point 80m from the base of the tower. (a). If the angle of elevation to the top of the tower of the wire is 28°, how long is the guy wire? (b). How tall is the tower? (4a). (4b). y x The wire is 90.6 m long and the tower is 42.5 m tall. 28o 80 m

(5). How tall is a bridge if a 6-foot-tall person standing 100 feet away can see the top of the bridge at an angle of elevation of 30° to the horizon? x The bridge is 57.7 + 6 or 63.7 ft tall 30o 100 ft 6 ft 100 ft

(6). A bow hunter is perched in a tree 15 feet off the ground. The angle of depression of the line of site to his prey on the ground is 30o. How far will the arrow have to travel to hit his target? 30o 15 x The arrow will travel 30 ft to its target. 30o

(7). Standing across the street 50 feet from a building, the angle to the top of the building is 40°. An antenna sits on the front edge of the roof of the building. The angle to the top of the antenna is 52°. a) How tall is the building? x The building is 42 ft tall. 40o 50 ft

(7). Standing across the street 50 feet from a building, the angle to the top of the building is 40°. An antenna sits on the front edge of the roof of the building. The angle to the top of the antenna is 52°. b) How tall is the antenna itself, not including the height of the building? y The antenna is 64.0 – 42.0 or 22 feet tall. 52o 50 ft

(8). An air force pilot must descent 1500 feet over a distance of 9000 feet to land smoothly on an aircraft carrier. What is the plane’s angle of descent? xo 1500 ft xo 9000 ft The angle of descent is approximately 9.5o.

Homework #1-7at bottom of Note Handout 1.5 Applications of Right Triangles

Applications of Right Triangles Section 1.5 Standard: MM2G2c