Chapter 9 Right Triangle Trigonometry DEFINE Sine, Cosine, & Tangent Ratios Use Ratios to SOLVE height and distance problems APPLY Vectors to Trigonometry Problems

Section 9 – 1 & 9 – 2 Tangent, Sine & Cosine Ratios Objectives: To write sine, cosine, and tangent ratios To find missing side lengths of right triangles using Trig Ratios To find missing angle measure of right triangles using Trig Ratios

Tangent Ratio Tangent of ∠𝑨= 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒆𝒈 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 ∠𝑨 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒆𝒈 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒕𝒐 ∠𝑨 Abbreviated Form: tan A = 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕

Sine Ratio Sine of ∠𝑨= 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒆𝒈 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 ∠𝑨 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 Abbreviated Form: sin A = 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆

Cosine Ratio Cosine of ∠𝑨= 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝒍𝒆𝒈 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 ∠𝑨 𝒍𝒆𝒏𝒈𝒕𝒉 𝒐𝒇 𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 Abbreviated Form: cos A = 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆

S O H C A H T O A INE OSINE ANGENT PPOSITE YPOTENUSE DJACENT YPOTENUSE

Example 1 Writing Tangent Ratios Write the Trig Ratios for each acute angle. A) B) How is tan K related to tan J?

How are Sin X and Cos Y related? Write the Trig Ratios for each acute angle. C) D) How are Sin X and Cos Y related?

HOMEWORK Kuta Ditto – Trig Ratios

Section 9 – 1 & 9 – 2 Continued… Objectives: To find missing side lengths of right triangles using Trig Ratios

Example 2 Finding Side Lengths Find the value of x. Round to the nearest tenth. A)

B) C)

D) E)

F) G)

H) I)

HOMEWORK KUTA Ditto; Solving Right Triangles

Section 9 – 1 & 9 – 2 Continued… Objectives: To find missing angles measures of right triangles using Trig Ratios

Example 3 Finding Angle Measures Find the m ∠ X or m ∠ Y to the nearest degree. A) B)

C) D)

E) F)