PROBLEM SOLVING ON ANGLE OF ELEVATION AND ANGLE OF DEPRESSION TRIGONOMETRIC RATIOS SOH-CAH-TOA. a. What trigonometric ratio are you going to use if you are going to find the measure of side t? a. TOA b. What trigonometric ratio are you going to use if you are going to find the measure of side q? a. SOH c. What trigonometric ratio are you going to use if you are going to find the measure of side l ? a. CAH D. What trigonometric ratio are you going to use if you are going to find the measure of side e? a. TOA STEPS IN SOLVING ANGLE OF ELEVATION AND ANGLE OF DEPRESSION A.Draw the diagram. B. What is/are given? C. What is to be determined? D. Formula used E. solution PROBLEM 1: A HIKER IS 400 METERS AWAY FROM THE BASE OF THE RADIO TOWER. THE ANGLE OF ELEVATION TO THE TOP OF THE TOWER IS 46°. HOW HIGH IS THE TOWER? A.Draw the diagram. B. What is/are given? C. What is to be determined? D. Formula used E. Solution A.Draw the diagram. B. What is/are given? Side b = 400 meters /adjacent π = 46° C. What is to be determined? Side a = height of the tower/opposite D. Formula used TOA πππππ ππ‘π tanπ = ππππππππ‘ Solution πππππ ππ‘π tan 46° = ππππππππ‘ π tan 46° = 400π π = π‘ππ46° π₯ 400π a= 1.0355303139 X 400m πππ π π = πππ. πππ οNote: A trigonometric ratio often helps us set up an equation, which can then be solved for the missing measurement. If two legs of the triangle are part of the problem, then it is a tangent ratio. If the hypotenuse is part of the problem, then it is either a sine or cosine ratio . PROBLEM 2: A LADDER IS LEANING AGAINST A WALL. THE FOOT OF THE LADDER IS 6.5 FEET FROM THE WALL. THE LADDER MAKES AN EAGLE OF 74° WITH THE LEVEL GROUND. HOW HIGH ON THE WALL DOES THE LADDER REACH? A.Draw the diagram. B. What is/are given? C. What is to be determined? D. Formula used E. Solution ο Problem 2: A ladder is leaning against a wall. The foot of the ladder is 6.5 feet from the wall. The ladder makes an eagle of 74° with the level ground. How high on the wall does the ladder reach? ο A.Draw the diagram. B. What is/are given? Foot of the ladder from the wall = 6.5ft π = 74° C. What is to be determined? Length of the ladder A. Formula use cos π = A.Solution Side b = ? Side c = 6.5ft π = 74° ππππππππ‘ βπ¦πππ‘πππ’π π ππππππππ‘ βπ¦πππ‘πππ’π π 6.5ππ‘ cos 74° = π 6.5ππ‘ π= cos 74° πππ π π = ππ. πππππ cos 74° = ο Problem 3: An airplane is flying at a height of 4 kilometers above the ground. The distance along the ground from the airplane to the airport is 6 kilometers. What is the angle of depression from the airplane to the airport? ο A.Draw the diagram . A. What is/are given? A. What is to be determined? A. Formula used A.Solution ο Problem 3: An airplane is flying at a height of 4 kilometers above the ground. The distance along the ground from the airplane to the airport is 6 kilometers. What is the angle of depression from the airplane to the airport? ο A.Draw the diagram . A. What is/are given? A. What is to be determined? Height of the plane above the ground = 4km Distance along the ground from the plane to the airport = 6km Angle of Depression from the airplane to the airport πππππ ππ‘π ππππππππ‘ A. Formula used tan π = A.Solution Side a = 4km Side b = 6km π =? πππππ ππ‘π ππππππππ‘ 4ππ tan θ = 6ππ tan θ = 0.6667 π½ = ππ. ππ° tan θ = Group1. The angle of elevation from a boat to the top of a 92-meter hill is 12°. How far is the boat from the base of the hill? Group2. From the top of a cliff 280 meters high, the angle of depression of a boat is 25°. How far from the base of the cliff is the boat? Group3. From a point 80m from the base of a tower, the angle of elevation to the top of the tower is 28°. How tall is the tower? Group4. A wire is attached to the top of the tower and to a point on the ground is 35m from the base of the tower. If the wire makes a 65° angle with the ground, how long is the wire? Group5. The angle of depression from the top of a tower to a boulder on the ground is 38°. If the tower is 25m high, how far from the base of the tower is the boulder? Evaluate In a ½ crosswise paper, use the table to illustrate and solve the problem. Problem1. A kite is flying at an angle of elevation 43°. Find the height of the kite if 37ft. of the string have been left out. Assignment: Problem: A ladder 8 meters long leans against the wall of a building. If the foot of the ladder makes an angle of 68° with the ground, how far is the base of the ladder from the wall? END THANK YOU FOR LISTENING
