This document discusses special angles and trigonometric ratios. It notes that special angles are called such because their trigonometric ratios can be determined without a calculator. It provides examples of the 30-60-90 and 45-45-90 right triangles and asks the reader to find values of variables in figures using simplest radical form if not an integer. It provides a word problem asking the reader to analyze what is being asked, draw the situation, and show the solution to find the height of a hot air balloon given the angle of elevation and distance to the observation point. It also asks the reader to study the meaning and difference between angle of elevation and angle of depression.

1. Lets play
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4. Trigonometric
Ratios of Special
Angles
 Find the trigonometric ratios of special
angles

8. a. Why do you think
these angles called
special?

9. b. How is the length of
the longer leg of a 30⁰-
60⁰-90⁰ triangle related
to the length of the
shorter leg?

10. c. How did you
determine the
trigonometric ratios
involving special angles?

11. Let’s Work
Together

12. The values of trigonometric ratios can be
determined even without the use of
calculator. Just be reminded that the two
special right triangles are the triangle
30° − 60° − 90° and the isosceles 45° −

13. Output #4.__
Directions: Find the value of each variable
used in the figures. If your answer is not an
integer, express it in simplest radical form.

16. Ass.# 4.__ Directions: analyze the problem to find what is being asked.
1. As a hot-air balloon began to rise, the ground crew
drove 1.2 miles to an observation station. The initial
observation from that instant is the angle between the
ground and the line of sight to the balloon is 30°.
Approximately how high was the balloon at that point?
Draw the situation. Show your solution.
2. Study: a. What is the meaning of angle of elevation?
Angle of depression?
b. How do they differ from each other?