Solving Right Triangle Application We have learned about the ratios for the six trig functions, so what can we do with these? Well we can use them to find missing angles and sides for any right triangle. As long as we know 2 of the parts to the trig ratio we can find the third part. For example if we know an acute angle and the opposite side we could use sine or cosecant to find the hypotenuse and we could use tangent or cotangent to find the adjacent side. Angle of depression In real life problems the angles are not called A,B and, C but instead we use the terms angle of elevation or depression. Building To find this angle – the angle of depression from 90 Angle of elevation Angles of elevation or depression are made with a horizontal line. Once you fill in the angles you can use trig ratios to find the sides.

Application problems: A ladder is leaning against the wall of a house the angle at which it touches the house is 220 if the foot of the ladder is 5.2 feet from the house. How tall is the ladder? Sin 220 = 5.2/x 220 x(sin 220) = 5.2 x = 5.2/sin220 x = 13.881 feet 5.2 feet

A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.30. To the nearest foot, how tall is the Washington Monument? Washington monument What trig ration can we use to find the height of the monument? Angle of elevation 78.30 x 115 feet

The angle of depression from the top of a building to a point on the ground is 46.50. To the nearest tenth, how far is the point on the ground to the top of the building if the building is 78 m high? Angle of depression What trig ration can we use to find the height of the monument? Building x 78 To find this angle – the angle of depression from 90 90 – 46.5 = 43.50

Practice #51) The tallest tower built before the era of television masts, the Eiffel Tower was completed on March 31, 1889. Find the height of the eiffel tower using the information given in the illustration. #62) A straight trail with an inclination of 170 leads from a hotel at an elevation of 9000 feet to a mountain lake at an elevation of 11200 feet. What is the length of the trail?

Practice time #54) A 22 foot ladder leaning against a building makes a 700 angle with the ground. How far up the building does the ladder reach?

Practice time 76) The eyes of a basketball player are 6 feet above the floor. The player is at the fre—throw line, which is 15 feet from the center of the basket rim. If the basket is 10 feet above the floor, what is the angle of elevation from the players eyes to the center of the rim?