Using Tangent, Sine and Cosine to find Sides of RIGHT TRIANGLES MODULE B- LESSON 5

1) Highlight sides of Right Triangle Hypotenuse, color right angle, highlight side across from right angle Adjacent, color given angle, highlight side touching it Opposite, highlight side opposite given angle 38o

2) Pick which tool to use x 15o 10 5 x 12o 20 17o x Reminder θ is a variable we use to represent the given angle! Tangent (TOA) Tanθ= Opposite 1 Adjacent Sine (SOH) Sinθ= Opposite 1 Hypotenuse Cosine (CAH) Cosθ= Adjacent 15o x 10 12o 5 x 17o 20 x

3) Solve for Missing Side How? Cross multiply and divide!! Round answers to the nearest tenth

Tangent- Example 1 (x on top) Q1 on your handout Tanθ= Opposite 1 Adjacent Tan(18º)= x 1 12 Cross multiply 12(Tan18) = x x = 3.9 18o x 12

Tangent- Example 2 (x on bottom) Not on your handout Tanθ= Opposite 1 Adjacent Tan(8º)= 14 1 x Cross multiply x(Tan8) = 14 divide both sides by (Tan38) to get x alone x = 14 (Tan8) x = 99.6 8o 14 x

Sine- Example 1 (x on top) Q1 on your handout Sinθ= Opposite 1 Hypotenuse Sin(12º)= x 1 5 Cross multiply 5(Sin12) = x x = 1.0 5 x 12o

Sine- Example 2 (x on bottom) Not on your handout Sinθ= Opposite 1 Hypotenuse Sin(38º)= 18 1 x Cross multiply x(Sin38) = 18 divide both sides by (Sin38) to get x alone x = 18 (Sin38) x = 29.2 18 x 38o

Cosine- Example 1 (x on top) Q1 on your handout Cosθ= Adjacent 1 Hypotenuse Cos(17º)= x 1 20 Cross multiply 20(Cos17) = x x = 19.1 20 17o x

Cosine- Example 2 (x on bottom) Q7 on your handout Cosθ= Adjacent 1 Hypotenuse Cos(16º)= 23 1 x Cross multiply X(Cos16) = 23 divide both sides by (Cos16) to get x alone X = 23 (Cos16) X = 23.9 x 16o 23

Review: All Right Triangle Tools Pythagorean Theorem (a2 + b2 = c2) c must be the hypotenuse Need: 2 sides Finds: 3rd side SOHCAHTOA (sine, cosine, tangent ratios) Need: 1 side, 1 angle Finds: 1 additional side