Do-Now 1. Use the Pythagorean Theorem to solve the following problem. Firefighters have a 17 foot extension ladder. In order to reach 15 feet up a building, how far away from the building should the foot of the ladder be placed? Convert each fraction to a decimal. Round to four decimal places

: Trigonmetric Ratios Objective: use sine, cosine and tangent ratios to find side lengths of triangles Homework: Practice Worksheet

Trigonometry The ratio of lengths of two sides of a right triangle You can only take the sine, cosine, and tangent of one of the acute angles of a right triangle. Real-life connection: Architecture, landscaping, construction, etc. (careers that use math, science and engineering)

Vocabulary to understand: Hypotenuse Opposite Adjacent X YZ

Finding lengths: Make sure calculator is in Radian mode not Degree

Sine (abbreviation: sin) X YZ *The opposite side is always across from the given angle. * The hypotenuse is always the side opposite of the right angle.

Cosine (abbreviation: cos) X YZ * The adjacent side is always next to or attached to the angle that is identified. It cannot be the hypotenuse.

Tangent (abbreviation: tan) X YZ

SOHCAHTOA 1.) 2.) 3.) 4.) 5.) 6.) A BC sin = cos = tan = Describe how the measures of two legs are related if the tangent of one of the acute angles is = 1.

Use your calculator and round to the nearest hundredth. 1.) sin 43 o = 2.) cos 72 o = 3.) tan 35 o =

Solve for the variable. 1.Start by asking yourself, what sides are the numbers and variables in relation to the given angle measure (adjacent side, opposite side or hypotenuse)? 2.Then ask, which trig function uses the sides you identified? 3.Set up the ratios based on S O H C A H T O A. opposite hypotenuse opposite adjacent hypotenuse adjacent

Solve for the variable. When the variable is on the bottom, divide (# ÷ trig function). When the variable is on the top, multiply (# x trig function). Tan 22˚=Cos 32˚= Sin 28˚= 3 ÷ Tan 20 = 10 x Cos 32 =15 x Sin 28 =

Real-life Connection A surveyor is finding the width of a river for a proposed bridge. A theodolite is used by the surveyor to measure angles. The distance from the surveyor to the proposed bridge site is 40 feet. The surveyor measures a 50 angle to the bridge site across the river. Find the length of the bridge to the nearest foot.

Review: Find the following and write the answers as fractions in simplest form and as decimals rounded to the four decimal places. 1. Sin P = 2. Cos P = 3. Tan P = Find the lengths of the legs. Round your answer to four decimal places