Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression

Super Math Student observes that the top of a building has an angle of elevation of 74° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building?

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 74° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? First, Let’s draw a picture. Obviously, the picture will not be drawn to scale.

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? First, Let’s draw a picture. Obviously, the picture will not be drawn to scale.

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? First, Let’s draw a picture. Obviously, the picture will not be drawn to scale. The triangle is the important part, not the artistic ability. But two things are missing.

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? First, Let’s draw a picture. Obviously, the picture will not be drawn to scale. The triangle is the important part, not the artistic ability. But two things are missing. x is the leg of the triangle we need to find, but notice the triangle is 4.5 feet above the ground. 6 inches is half a foot, so 4’6” is 4.5 feet.

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? sin, cos, or tan?

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? sin, cos, or tan? The adjacent side is 228 feet, the opposite side is x.

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? sin, cos, or tan? The adjacent side is 228 feet, the opposite side is x. SOH CAH TOA

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? sin, cos, or tan? The adjacent side is 228 feet, the opposite side is x. SOH CAH TOA The triangle chose tan for us, because we are working with the adjacent and opposite sides.

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building?

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? Hopefully we have become proficient with a calculator to solve this type of proportion with trig functions. Be sure to be set for degrees and use the correct function.

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? The building is about feet tall.

Geometry Day 13 Thu. March 17 / Mon. March 21 Angles of Elevation and Depression Super Math Student observes that the top of a building has an angle of elevation of 37° when viewed on a line of sight. Super Math Student is standing 228 feet from the building. Super Math Student’s eye is exactly 4’6” above the ground. How tall is the building? The building is about feet tall. Word questions should have word answers.

An airplane is flying 2 miles above the ground, when the pilot looks out the window, and notices that the base of a tree is at a 12° angle of depression. How far does the airplane need to fly before it will be directly above the tree? So here is a picture for the problem, with the 2 miles and 15°. Let’s label one side with x and complete the triangle. sin, cos, or tan? Well, opposite is 2, and adjacent is x...

An airplane is flying 2 miles above the ground, when the pilot looks out the window, and notices that the base of a tree is at a 12° angle of depression. How far does the airplane need to fly before it will be directly above the tree? I do not like having x in the denominator. I multiplied both sides by x. Then I divided both sides by tan15.

An airplane is flying 2 miles above the ground, when the pilot looks out the window, and notices that the base of a tree is at a 12° angle of depression. How far does the airplane need to fly before it will be directly above the tree? Word questions should have word answers. The airplane will be above the tree in about 7.5 miles

Looking down at partially frozen Narada Falls, Mount Rainier National Park.