 # Use Pythagorean Theorem: x = 12.68 = 12.7 rounded This is a 30-60-90 Triangle: ON A SHEET OF PAPER.

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Use Pythagorean Theorem: x = 12.68 = 12.7 rounded This is a 30-60-90 Triangle: ON A SHEET OF PAPER

Right Triangle Trigonometry Mr. Miller Standard addressed: Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.

VERY IMPORTANT: YOU MUST SET YOUR CALCULATOR TO DEGREE Press Mode key Set to DEGREE

All Scientific Calculators have a DEGREE or DEG setting Make sure you know how to set your personal calculator. If you need help let Mr. Miller know Click here to use Online Calculator

Adjacent Opposite Side Hypotenuse of a Right Angle Triangle. Terms you need to be familiar with!!!

Adjacent side Opposite side  Hypotenuse This is the Greek letter Theta. It is used to represent an unknown angle.

 Hypotenuse Adjacent side Opposite side

Naming Sides of Right Triangles   

Warm – up: Find the missing measures. Write all answers in radical form. 45° x w 7 60° 30° 10 y z Session 17

The Trigonometric Functions we will be looking at SINE COSINE TANGENT

The Trigonometric Functions SINE COSINE TANGENT

SINE Prounounced “sign”

Prounounced “co-sign” COSINE

Prounounced “tan-gent” TANGENT

Prounounced “theta” Greek Letter  Represents an unknown angle

Sin, Cos, Tan Buttons Sine, Cosine, Tangent These are the three basic Trig ratios (fractions) used to solve for sides and angles in right triangles.

We need a way to remember all of these ratios…

Old Hippie Some Old Hippie Came A Hoppin’ Through Our Apartment

SOH CAH TOA Old Hippie Sin Opp Hyp Cos Adj Hyp Tan Opp Adj

Finding sin, cos, and tan

Table of Trigonometric Ratios Solve for x: Sin 18 = x Cos x =.6157 Tan 76 = x ◦ ◦ ◦ x =.3090 x = 52 ◦ x = 4.0108

 Definition of Sine Ratio.Sine Ratio For any right-angled triangle Sin  = Opposite side Hypotenuse (SOH)(SOH)

A B C 15 8 Find the sine of  A and  B 17

6 8 10 SOH CAH TOA

Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 9 6 10.8 A

Find the values of the three trigonometric functions of . 4 3 ? Pythagorean Theorem: (3)² + (4)² = c² 5 = c 5

Find the sine, the cosine, and the tangent of angle A A 24.5 23.1 8.2 B Give a fraction and decimal answer (round to 4 decimal places).

Finding a side

A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? 50 71.5° ? tan 71.5° y = 50 (tan 71.5°) y = 50 (2.98868) Ex.

A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? 200 x Ex. 5 60° cos 60° x (cos 60°) = 200 x X = 400 yards

Now you know three ways to find parts of a right triangle: 1.Pythagorean Theorem – If you know two sides, then use to find the third side. 2.Special Right Triangles- If it is a 30-60-90 or 45-45-90, then follow the pattern to find the side lengths. 3.Right Triangle Trigonometry- Use Sin, Cos, and Tan (Soh Cah Toa) ratios to solve for sides and angles of a right triangle.

HOMEWORK Complete the 7.3 Packet

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