Name: ______________________________________________ Period: _________G 4-1

G4a. I can use appropriate tools to find missing sides and angles in right trianglesG4a. I can identify slope triangles and use tangent to solve for missing side lengths. Slope Triangle: A slope triangle is a right triangle that has its hypotenuse on the line that contains it.

Calculate the slope ratio of the line using the threedifferent slope triangles.

1. ∆ y∆x

=23 2. 3.

Are they all the same? Why? Are the triangles similar? Why?

For each graph, draw three slope triangles. Calculate the slope ratio for each one. 1) 2)

3) 4)

5) What do all of these graphs have in common? How do you know?

6) Examine the triangles you drew in problems 1-4. What angles are always the same? Which one’s change? How do you know?

It turns out that our ratio is closely linked to the tangent function. Tangent is a special function that relates the angle in a triangle to the ratio of the opposite side divided by the adjacent side. In other words,

tan ( x )= oppositeadjacent

Using the information in the diagram, solve for the missing side using the tangent button in your calculator. 7) 8)

9) 10) Careful….

11) 12)

13) A ladder makes a 75o angle with the wall it is leaned against. The base of the ladder is 5 feet from the wall. How high up does the ladder reach?