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Drill Find the missing side length of right triangle ABC. Assume side C is the hypotenuse. 1.A = 7, B = 3 2.A = 9, C = 15
Section 4.2 Students will calculate trig ratios.
What is Trig? Based on similar triangles Used to find an unknown angle or side length of a triangle Uses ratios
Trig Functions A c b B a C The six trig ratios:
Just Remember: SOH CAH TOA It means: –Sin = opp/hyp –Cos = adj/hyp –Tan = opp/adj
Find the six trig ratios of angle A in the following right triangle. A 12 B 8 C
Calculate the six trig ratios of angle A and angle C in the following right triangle. A 4 5 B 3 C
Special Right Triangles 30-60-90 x√3 2x x 30 60
Find all sides, then calculate six trig ratios of angle A. A 30 60 B 5 C
Special Right Triangles 45-45-90 A x x √2 B xC
Find all sides, then calculate six trig ratios of angle A. 12 A B C
Use your calculator to calculate: sin 65° cos 125° tan 15° sec 325° csc 230° cot 212°
Use your calculator to calculate sin cos tan csc sec cot
Example Let Ө be an acute angle such that sin Ө = 5/6. Evaluate the other five trig functions of Ө.
Example Let Ө be an acute angle such that sec Ө = 12/5. Evaluate the other five trig functions of Ө.
Solve the right triangle ABC for all of its unknown parts. A = 20 degrees, a = 12.3 B = 55 degrees, a = 15.58 A = 35 degrees, c = 15 B = 48 degrees, b = 7 C A B
Evaluate without using a calculator
Problem Solving with Trig An angle of elevation is the angle through which the eye moves up from horizontal to look at something above. Angle of Elevation
Problem solving An angle of depression is the angle through which the eye moves down from horizontal to look at something below. Angle of depression
Example From a point 340 feet away from the base of the Peachtree Center Plaza in Atlanta, Georgia, the angle of elevation to the top of the building is 65 degrees. Find the height of the building.
Example The angle of depression of a buoy from the top of a lighthouse 130 feet above the surface of the water is 6 degrees. Find the distance from the base of the lighthouse to the buoy.
Example A tree casts a shadow 51 feet long when the angle of elevation of the sun (measured with the horizon) is 25 degrees. How tall is the tree?
Homework Read 4.2, do #s 1 – 53 odd, 61, 65
Jeopardy Trig ratios Finding a missing side Finding a missing angle Sec, csc, and cot Word Problems
Right Triangle Trigonometry
Section Review right triangle trigonometry from Geometry and expand it to all the trigonometric functions Begin learning some of the Trigonometric.
Applications Involving Right Triangles
TRIGONOMETRY OF RIGHT TRIANGLES. TRIGONOMETRIC RATIOS Consider a right triangle with as one of its acute angles. The trigonometric ratios are defined.
Chapter 9. COMPLETE THE RATIO: Tan x = _____ x.
Old stuff will be used in this section › Triangle Sum Theorem The sum of the measures of the angles in a triangle is 180° › Pythagorean Theorem
6/10/2015 8:06 AM13.1 Right Triangle Trigonometry1 Right Triangle Trigonometry Section 13.1.
1 Right Triangle Trigonometry Pre-Calculus Day 38.
Right Triangle Trigonometry. Objectives Find trigonometric ratios using right triangles. Use trigonometric ratios to find angle measures in right triangles.
Given that and find the value of the cos θ. Memorize it! Quiz 1 st week of 2 nd semester ◦ 8 minute time limit ◦ All or nothing ◦ 20 points
Section To identify the “parts” of a right triangle 2. To learn the “definitions” (formulas) for each of the trigonometric functions 3. To find.
Trig ratios of acute angles: You will be able to state the 6 trig ratios for an acute triangle and solve related problems. Reciprocal Trig Functions.
Trigonometry. Logarithm vs Natural Logarithm Logarithm is an inverse to an exponent log 3 9 = 2 Natural logarithm has a special base or e which equals.
Solving Trig Problems Precal – Sections Reference Angles p. 280 Associated with every angle drawn in standard position there is another angle.
Pre-AP Pre-Calculus Chapter 4, Section 2 Trigonometric Functions of Acute Angles
Trigonometry. Basic Ratios Find the missing Law of Sines Law of Cosines Special right triangles
Sec 6.2 Trigonometry of Right Triangles
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