Angles of Elevation & Depression

What are we learning today? Standard: MCC9-12.G.SRT.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. Skills: SWBAT recognize angles of elevation and depression SWBAT set up word problems using trigonometric ratios SWBAT solve problems involving angles of elevation and depression using SOHCAHTOA

Skills Check

Let’s review the vocabulary! Don’t worry about writing this down in your notes. What word do you think of when you hear the word elevate or elevation? What word do you think of when you hear the word depression? depressed elevator

How can you tell if the angle is an angle of elevation or depression? Place your finger on the vertex of the angle. Trace along the nonhorizontal side of the angle. See if your finger is above the vertex (elevation) or below the vertex (depression).   Let’s Break it Down! Step 1: Put your finger on the vertex(where the 2 lines meet). Step 2: Identify the nonhorizontal line(the line that is not straight). Then trace your finger along the line. Step 3: If your finger is going down, then it’s an angle of depression. If your finger is going up, then it’s an angle of elevation. Vertex: a corner or a point where lines meet

Depression and Elevation horizontal angle of depression line of sight angle of elevation horizontal Discuss alternate interior angles & how top angle makes a 90 degree angle

What is a description of angle 1 as it relates to the situation shown? I Do: Ms. Massih will complete the following problem. Make sure you have your pencils down, mouths closed, and eyes up at the board while she is doing the problem. You will have time to copy down the problem after I have finished the problem. What is a description of angle 1 as it relates to the situation shown? Angle 1 is below the vertex, so angle one is the angle of depression from the bird to the person in the hot air balloon. What is a description of angle 4 as it relates to the situation shown? You end up above the vertex, so angle 4 is the angle of elevation from the base of the mountain to the person in the hot-air balloon.

Your Turn! Work quietly with your group members on the following problem. We will review the answer as a class after. Remember, ask your group members before you ask the teacher! What is a description of angle 2 as it relates to the situation shown?

Classify each angle as angle of elevation or angle of depression.

Example 2 Over 2 miles (horizontal), a road rises 300 feet (vertical). What is the angle of elevation to the nearest degree? 5280 feet – 1 mile

Example 3 Find the angle of elevation to the top of a tree for an observer who is 31.4 meters from the tree if the observer’s eye is 1.8 meters above the ground and the tree is 23.2 meters tall. Round to the nearest degree.

Example 4 A construction worker leans his ladder against a building making a 60o angle with the ground. If his ladder is 20 feet long, how far away is the base of the ladder from the building? Round to the nearest tenth.

Groupwork Work on the next 6 problems with your group members. Remember to ask your group members before you raise your hand to ask for help from the teacher. We will review the answers in about 10 minutes.

Practice #1 The angle of depression from the top of a tower to a boulder on the ground is 38º. If the tower is 25m high, how far from the base of the tower is the boulder? Round to the nearest whole number.

Practice #2 A 75 foot building casts an 82 foot shadow. What is the angle that the sun hits the building? Round to the nearest degree.

Practice #3 A boat is sailing and spots a shipwreck 650 feet below the water. A diver jumps from the boat and swims 935 feet to reach the wreck. What is the angle of depression from the boat to the shipwreck, to the nearest degree?

Practice #4 A 5ft tall bird watcher is standing 50 feet from the base of a large tree. The person measures the angle of elevation to a bird on top of the tree as 71.5°. How tall is the tree? Round to the tenth.

Practice #5 A block slides down a 45 slope for a total of 2.8 meters. What is the change in the height of the block? Round to the nearest tenth.

Practice #6 A projectile has an initial horizontal velocity of 5 meters/second and an initial vertical velocity of 3 meters/second upward. At what angle was the projectile fired, to the nearest degree?

Independent Practice Work quietly on the problems on the next page independently. You will be turning this in before you leave class.