Warm Up 1. Prove or disprove point A lies on the circle that is centered at point B and contains point C. 2.

DERIVED FROM THE ANCIENT GREEK LANGUAGE AND MEANS THE MEASUREMENT OF TRIANGLES. Trigonometry

Measurement of Triangles Sides Ways we already know: Pythagorean Theorem Congruent Triangles Similar Triangles Angles Ways we already know: Triangle Sum Theorem Congruent Triangles Similar Triangles

Vocabulary we need…

Labeling a right triangle

For any right triangle, six ratios of pairs of sides are possible. This year we will study 3 of the ratios.

Sine ratio The sine of A … The sine of B …

In ∆ ABC, find the following…

Cosine ratio The cosine of A … The cosine of B …

In ∆ ABC, find the following…

Tangent ratio The tangent of A … The tangent of B …

In ∆ ABC, find the following…

A little help to remember…. SOHCAHTOA SOH - Sine, Opposite leg, Hypotenuse CAH - Cosine, Adjacent leg, Hypotenuse TOA - Tangent, Opposite leg, Adjacent leg

Let’s practice… Making Practice Fun 81

Using angle measures Since corresponding sides of similar triangles are proportional, the sine ratio is the same in any right triangle. This is true for any trigonometric value of an angle in a right triangle. The values for any angle measures can be found using a calculator.

Calculators Make sure that your calculator is in degree mode

You can find the measure of an angle if one of its trigonometric values is known. Example 1 : Example 2:

Guided Practice Making Practice Fun 82

Solving Right Triangle Problems In ∆ ABC, m<B = 61°, c = 20, find b. b = 17.5

Solving Right Triangle Problems In ∆ ABC, m<B = 42°, c = 10, find b. b = 6.7

Solving Right Triangle Problems In ∆ ABC, m<A = 39°, b = 20, find a. a = 7.3

Finding an angle measure Find the m<A? What trig function? 23.9°

Angle of Elevation/ Angle of Depression

The angle of elevation of an airplane is 12°. The distance to the plane is 16 km. How high is the plane? 3.3 km

A fire warden’s tower is 43 m tall. The angle of depression from the window of the tower to a fire in the woods is 5°. How far away from the base of the tower is the fire? 491 m

Guided practice 1. A kite is flown with 210 m of string. The angle of elevation of the kite is 61°. How high is the kite? 2. The top of a lighthouse is 110 m above the level of the water. The angle of depression from the top of the lighthouse to a fishing boat is 18°. How far is the base of the lighthouse is the fishing boat? 3. A mountain trial slopes upward at an angle of 5°. A hiker hikes four miles up the trail. How much altitude does the hiker gain? m m 0.35 km

Assignment Making Practice Fun 83 “Big Grass Field” Puzzle