By who? Ancient Egyptians Hipparchus in 150BC
Real-world Problem A 5-foot tall woman stands 15 feet from a flagpole; she casts a shadow 7 feet long which ends at exactly the same point as the shadow of the flagpole. How tall is the flagpole? Solution From the picture above, if h represents the height of the flagpole,. Multiplying both sides of this equation by 22 yields the result: feet. That is, the flagpole is about 15.7 feet tall
Real-world Problem The angle of elevation from the bottom of a ski lift to the top of a mountain is 28°. If a skier rides a distance of 900 ft. on this ski lift to get to the top of the mountain, what is the vertical distance d from the bottom of the ski lift to the top of the mountain?
Real-world Problem A pilot must approach an airport at a descent angle (angle of depression) of 11° toward the runway. If the plane is flying at an altitude of 3200 ft, at what distance d (in miles measured along the ground) should the pilot start the descent? (remember that there are 5280 feet in one mile).
Real-world Problem A tent is supported by a cable stretched between two poles at a height of 80 inches. The sides of the tent make an angle of 58° with the ground. How wide is the tent at the bottom?
Further exploration Sosmath.com/trig Project: Width of a Stream If your schoolyard does not have a stream, it probably has some other feature that would be hard to measure such as a gully or ravine. Find a prominent feature -- like a trashcan -- on one side, then pace upstream 50 feet on the other side of the feature and measure the angle across the stream to the prominent feature. The width of the stream is 50 times the tangent of the angle.