Math 2Name ______

Lesson 5-1:Right Triangle TrigonometryDate ______

Learning Goals:

  • I can use the Pythagorean Theorem to solve for an unknown side length of a right triangle.
  • I can use the characteristics of similar figures to justify the trigonometric ratios.
  • I can define the following trigonometric ratios for acute angles in a right triangle: sine, cosine,

and tangent.

  • I can calculate sine, cosine and tangent ratios for acute angles in a right triangle when given two

side lengths.

  • I can understand that if cos A = sin B, then A and B are complementary angles. I can explain

this using a picture of a right triangle.

  • I can use the angle measures to estimate side lengths.
  • I can use side lengths to estimate angle measures.

I.Prerequisite Skills for Trigonometry:

II.What is Trigonometry?

Trigonometry is

Vocabulary and symbols:

Opposite leg

Adjacent leg

Hypotenuse

Acute anglesα β θ

Right angle

Pythagorean Theorem

Ratio

Complementary angles

OVER 

Page 2

III.Ratios of Sides in Right Triangles

Verify that the four triangles above are similar and write the similarity statements.

Round to the nearest 1000th.

Length of the leg opposite the 22° angle / Length of the leg adjacent tothe 22° angle / Length of the hypotenuse / Length of opposite leg
÷
Length of adjacent leg / Length of opposite leg
÷
Length of hypotenuse / Length of adjacent leg
÷
Length of hypotenuse
ΔABC
ΔDEF
ΔHIJ
ΔLMN

Calculate the

mean of each

column.

Page 3

1.On the calculator, press c and choose #5 Settings and #2 Document Settings. Next scroll down to Angle and choose Degree. Finally select Make Default.

2.Use your calculator to fill in the problems below: Round to 3 decimal places.

Look back at your computations in the table. Where do you see these same values?

3.Based on your measurements and computations from this worksheet complete the following definitions:

In any right triangle, where is NOT the right angle:

sine

cosine

tangent

4. Mnemonic device to remember these ratios:

5.If you know a ratio of two side lengths, how can you find the acute angle measure?

In the figure belowis a right angle. Round to 3 decimal places.

  • Find the length of c using

5.8 cm

29◦

  • Find the length of c using
  • What is the relationship betweenand

Practice

1. Find the below ratios:2.Solve for x

1a.

1b.3.Solve for

1c.

HOMEWORK:

7. 8.

7. 8. 9.

C. Solve for the variables. Round to the nearest 100th.

OVER 

4. 5.

6. 7.