OBJECTIVE:TO SOLVE RIGHT TRIANGLE PROBLEMS USING THE TRIG FUNCTIONS. USING THE RATIOS UNIT 10: SECTION 8.7.

Slides:

Advertisements

Similar presentations

Solving Right Triangles Essential Question How do I solve a right triangle?

Advertisements

Section 7.6 Apply the Sine and Cosine Rations.

Warm-Up Exercises 2. Name the leg opposite X. 1. Name the hypotenuse. Use this diagram for Exercises 1-4. ANSWER YZ ANSWER XZ.

5/5/ : Sine and Cosine Ratios 10.2: Sine and Cosine Expectation: G1.3.1: Define the sine, cosine, and tangent of acute angles in a right triangle.

Warm Up Find the unknown length for each right triangle with legs a and b and hypotenuse c. NO DECIMALS 5. b = 12, c =13 6. a = 3, b = 3 a = 5.

9.6 Solving Right Triangles Geometry Mrs. Spitz Spring 2005.

Trigonometry Chapters Theorem.

Solving Right Triangles

8.3 Solving Right Triangles

EXAMPLE 1 Use an inverse tangent to find an angle measure

EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation.

EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation.

EXAMPLE 1 Finding Trigonometric Ratios For PQR, write the sine, cosine, and tangent ratios for P. SOLUTION For P, the length of the opposite side is 5.

 In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs  a 2 + b 2 = c 2 a, leg.

A B C Warm UP What side is The hypotenuse? What side is opposite  A?

Geometry Notes Lesson 5.3B Trigonometry

Friday, February 5 Essential Questions

Use this diagram for Exercises 1–4.

Write each fraction as a decimal rounded to the nearest hundredth.

EXAMPLE 3 Solve a right triangle

Finding an angle. (Figuring out which ratio to use and getting to use the 2 nd button and one of the trig buttons. These are the inverse functions.) 5.4.

7-7 Solving Right Triangles Geometry Objectives/Assignment Solve a right triangle. Use right triangles to solve real-life problems, such as finding the.

The midpoint of is M(-4,6). If point R is (6, -9), find point J.

Chapter 7.7 Notes: Solve Right Triangles Goal: You will use inverse tangent, sine, and cosine ratios to determine the unknown angle measures of right triangles.

SECTION 8.4 TRIGONOMETRY. The word trigonometry comes from two greek terms, trigon, meaning triangle, and metron, meaning measure. a trigonometric ratio.

Chapter 13 Sec 1 Right Triangle Trigonometry 2 of 12 Algebra 2 Chapter 13 Section 1 The ratios of the sides of the right triangle can be used to define.

Apply Sine and Cosine Ratios 5.3 (M2). Vocabulary Sine and Cosine ratios: trig. Ratios for acute angles with legs and hypotenuse C B A.

Apply the Sine and Cosine Ratios

EXAMPLE 4 Find a hypotenuse using an angle of depression SKIING

Chapter 7 – Right Triangles and Trigonometry

Set calculators to Degree mode.

Warm-Up Determine whether the following triangles are acute, right or obtuse. 1. 7, 10, , 8, , 5, 6.

EXAMPLE 3 Standardized Test Practice SOLUTION In the right triangle, you are given the lengths of the side adjacent to θ and the hypotenuse, so use the.

EXAMPLE 3 Solve a right triangle Solve the right triangle. Round decimal answers to the nearest tenth. SOLUTION STEP 1 Find m B by using the Triangle Sum.

8-4 Trigonometry, day 2 You used the Pythagorean Theorem to find missing lengths in right triangles. Find trigonometric ratios using right triangles. Use.

EXAMPLE 2 Find cosine ratios Find cos U and cos W. Write each answer as a fraction and as a decimal. cos U = adj. to U hyp = UV UW = cos W.

Solving Right Triangles Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems.

Warm-Up Write the sin, cos, and tan of angle A. A BC

Warm-Up Exercises ANSWER 8.0 ANSWER If m P = 58° and r = 5, find p. 1. If PR = 12 and m R = 19°, find p. Use this diagram for Exercises 1–4.

Using trig ratios in equations Remember back in 1 st grade when you had to solve: 12 = x What did you do? 6 (6) 72 = x Remember back in 3rd grade when.

Date: Topic: Trigonometry – Finding Side Lengths (9.6) Warm-up: A B C 4 6 SohCahToa.

Then/Now You evaluated functions. (Lesson 1-1) Find values of trigonometric functions for acute angles of right triangles. Solve right triangles.

EXAMPLE 1 Use an inverse tangent to find an angle measure Use a calculator to approximate the measure of A to the nearest tenth of a degree. SOLUTION Because.

Trigonometric Ratios How do you use trig ratios? M2 Unit 2: Day 4.

Section 9.5: Trigonometric Ratios. trigonometric ratio – a ratio of the lengths of two sides of a right triangle. The three basic trigonometric ratios.

trigonometric functions sine cosine tangent cosecant secant cotangent

Use the tangent of an acute angle to find a leg length.

Find the values of the variables.

Use this diagram for Exercises 1–4.

9.6 Solving Right Triangles

Use the diagram for Exercises 1-4.

EXAMPLE 2 Find cosine ratios

…there are three trig ratios

Inverse Trigonometric Functions

7-7 Solving Right Triangles

Use this diagram for Exercises 1-4.

Solving Right Triangles

9.6 Solving Right Triangles

…there are three trig ratios

Right Triangle Trigonometry

Use this diagram for Exercises 1-4.

Using Right Triangles in the Real World

EXAMPLE 1 Find sine ratios

Solving Right Triangles -- Trig Part III

Warm – up Find the sine, cosine and tangent of angle c.

Check point P #4 # P 461 #4 # 8.

Right Triangle Trigonometry

Geometry Section 7.7.

…there are three trig ratios

Presentation transcript:

OBJECTIVE:TO SOLVE RIGHT TRIANGLE PROBLEMS USING THE TRIG FUNCTIONS. USING THE RATIOS UNIT 10: SECTION 8.7

EXAMPLE 4 Find a hypotenuse using an angle of depression SKIING You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21 o. About how far do you ski down the mountain?

EXAMPLE 4 Find a hypotenuse using an angle of depression SOLUTION sin 21 o Write ratio for sine of 21 o. sin 21 o Substitute. x sin 21 o = 1200 Multiply each side by x. x = sin 21 o Divide each side by sin 21 o x Use a calculator to find sin 21 o x Simplify. opp hyp = 1200 x = ANSWER You ski about 3348 meters down the mountain.

GUIDED PRACTICE for Example 4 6 Suppose the angle of depression in Example 4 is 28°. About how far would you ski? WHAT IF ? SOLUTION sin 28 o Write ratio for sine of 28 o. sin 28 o Substitute. x sin 28 o = 1200 Multiply each side by x. x = sin 28 o Divide each side by sin 28 o opp hyp = 1200 x =

GUIDED PRACTICE for Examples 4 x Use a calculator to find sin 28 o x 2556m Simplify.

EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse DOG RUN You want to string cable to make a dog run from two corners of a building, as shown in the diagram. Write and solve a proportion using a trigonometric ratio to approximate the length of cable you will need.

EXAMPLE 3 Use a trigonometric ratio to find a hypotenuse SOLUTION sin 35 o = opp hyp Write ratio for sine of 35 o. sin 35 o = 11 x Substitute. x sin 35 o = 11 Multiply each side by x. x = 11. sin 35 o Divide each side by tan. 35 o x Use a calculator to find tan. 35 o x 19.2 Simplify. ANSWER You will need a little more than 19 feet of cable.

EXAMPLE 3 Solve a right triangle Solve the right triangle. Round decimal answers to the nearest tenth. SOLUTION STEP 1 Find m B by using the Triangle Sum Theorem. 180 o = 90 o + 42 o + m B 48 o = m B

EXAMPLE 3 Solve a right triangle STEP 2 Approximate BC by using a tangent ratio. tan 42 o = BC 70 Write ratio for tangent of 42 o. 70 tan 42 o = BC Multiply each side by 70. Approximate tan. 42 o BC 63 BC Simplify and round answer.

EXAMPLE 3 Solve a right triangle STEP 3 Approximate AB by using a cosine ratio. cos 42 o = 70 AB Write ratio for cosine of 42 o. AB cos 42 o = 70 Multiply each side by AB. Divide each side by cos. 42 o Use a calculator to find cos. 42 o AB 70 cos 42 o = AB AB 94.2 Simplify. ANSWER The angle measures are 42 o, 48 o, and 90 o. The side lengths are 70 feet, about 63 feet, and about 94 feet.

EXAMPLE 4 Solve a real-world problem THEATER DESIGN Suppose your school is building a raked stage. The stage will be 30 feet long from front to back, with a total rise of 2 feet. A rake (angle of elevation) of 5 o or less is generally preferred for the safety and comfort of the actors. Is the raked stage you are building within the range suggested?

EXAMPLE 4 Solve a real-world problem SOLUTION Use the sine and inverse sine ratios to find the degree measure x of the rake. sin x o = opp. hyp = x sin – ANSWER The rake is about 3.8 o, so it is within the suggested range of 5 o or less.