4.2a: Right Triangle Trigonometry p GSE’s Covered Primary: M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, circles, or right triangle ratios (sine, cosine, tangent) within mathematics or across disciplines or contexts (e.g., Pythagorean Theorem, Triangle Inequality Theorem). Secondary: M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope.

Using the reference angle for the right triangles above, identify: adjacent side, opposite side, hypotenuse. Reference angle- an acute angle used in the right triangle

SOHCAHTOA All are sides of right triangles Replace this With either the angle Or variable

What does it mean? The sine of the reference angle is the ratio of the opposite side to the hypotenuse of a right triangle. x The angle we are talking about The opposite side to the angle we are talking about Always the hypotenuse in a right triangle 8 in 9 in So, sin x = Lets solve this equation

x A B C 4 in 10 in To solve for the angle, we need to get rid of sin To get rid of sin and solve for the angle we use on both sides Which means the angle is about 24 degrees

50 6 in x Solve for x Label the information you have in the triangle Reference angle Adjacent Side to The ref angle hypotenuse If we have the Adjacent side and the Hypotenuse, think SOHCAHTOA Now solve For x Multiple both sides by x Divide both sides by Cos 50 Which means the hypotenuse is 9.3 in

70 8 ft X ft Solve for x Label the information you have in the triangle If we have the Opposite side and the Adjacent, think SOHCAHTOA Adjacent side to the ref angle Opposite side to the ref angle Multiply both sides by 8 You have x alone, so evaluate 8 tan 70 So the opposite side is approximately 22 ft

Example on the coordinate plane A (8,2) B (4,5) C (7,9) Secondary: M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope. Primary: M(G&M)–10–2

Solve for the missing sides of the triangle using 2 different methods. Show all work

NECAP released Item 2007

Find the area of the triangle

Find the Volume of the Prism

Phil stands on the sidewalk of a road. Phil’s favorite pizza restaurant is on the other side of the road. His estimated line of sight to the pizza place is 43 degrees. He needs to go to the post office at some point which is 120 feet up the road he is standing on. The line of sight from the post office to the pizza place is 90 degrees. How far of walk would it be for Phil from his original position to the pizza place? How far is the walk from the post office to the pizza place?

Homework