Pretest Please complete the pretest for this standard on your own. Try to remember all you can from our first discussion of this topic.

Define and use the trigonometric ratios (sine, cosine, tangent, cotangent, secant, cosecant) in terms of angles of right triangles. MA.912.T.2.1

LEQ: How do I use trigonometric ratios to find angles and sides of right triangles? Vocabulary _____ sine of an angle _____ cosine of an angle _____ tangent of an angle _____ hypotenuse Matching A.The side opposite the right angle of a right triangle B. The ratio of the side opposite the angle to the side adjacent to the angle C. The ratio of the side opposite the angle to the hypotenuse of the triangle D. The ratio of the side adjacent the angle to the hypotenuse of the triangle C D B A

I do… Basic Trigonometric Ratios 1. You have to find a side given another side and an angle. In this case, you will calculate the value of the trig function evaluated at the given angle and then solve for the missing side. 2. You have to find the angle given two sides of a right triangle. In this case you need to use the inverse trig function. This is found by using the “second” or “shift” key on your calculator. There are two types of trig problems.

I do… Basic Trigonometric Ratios Refer to right triangle ABC In order to find the cosine, we need to know the hypotenuse. You may recognize that this is a Pythagorean triple, and that the hypotenuse is 13. Otherwise, you can apply the Pythagorean Theorem to find the hypotenuse. 13

I do… Angles of Elevation and Depression If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the angle of depression. horizontal Angle of depression Angle of elevation The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line from the object to the observer's eye (the line of sight). Notice that the angle of elevation and the angle of depression are alternate interior angles and are EQUAL!

I do… Draw a picture to solve a word problem A kite is held by a taut string pegged to the ground. The string is 40 feet long and makes a 33 degree angle with the ground. Supposing that the ground is level, find the vertical distance from the ground to the kite. 40 feet 33 degrees Draw a picture. Set up a ratio and solve. x

I do… Real World Application The driver of the boat wants to change direction to sail toward the restaurant. Which of the following is closest to the value of x? A tackle shop and restaurant are located on the shore of a lake and are 32 meters (m) apart. A boat on the lake heading toward the tackle shop is a distance of 77 meters from the tackle shop. This situation is shown in the diagram below, where point T represents the location of the tackle shop, point R represents the location of the restaurant, and point B represents the location of the boat. This problem has a LOT of text, but it really is just a basic trig ratio problem. The hypotenuse is not labeled in this problem, only the sides opposite and adjacent to x. This must be a tangent problem.

I do… Real World Application Mr. Rose is remodeling his house by adding a room to one side, as shown in the diagram below. In order to determine the length of the boards he needs for the roof of the room, he must calculate the distance from point A to point D. In this problem, we are given an angle, and asked to find a side, so we will not need to use an inverse function opposite Hypotenuse = x The trig function that uses opposite and hypotenuse is sine.

We do Sage and Scribe

We do Pick a Card With your partner, takes turns picking a card. The student that picked the card shares it with their partner and offers the explanation or solution. The other student verifies for accuracy, then picks a card to take their turn.

You Do 1. Find the value of w, then x. Round length to the nearest tenth and angle measures to the nearest degree. 2. Find the angle of elevation of the sun from the ground to the top of a tree that is 10 yards tall casts a shadow 14 years long. Round to the nearest degree. 3. Find the value of x.

You Do 1. Find the value of w, then x. Round length to the nearest tenth and angle measures to the nearest degree.

You Do 2. Find the angle of elevation of the sun from the ground to the top of a tree that is 10 yards tall casts a shadow 14 years long. Round to the nearest degree

You Do 3. Find the value of x. The angle of elevation is also 10. We use the sine function.

Post Test Please complete the post test for this standard on your own. Do the best you can, hopefully you will show improvement over your pretest score.