Lesson 7: Right Triangles and Trig Test

Right Triangles and Trigonometry Overview

• Triangle with side lengths 34 in, 20 in, 47 in is classified as obtuse.
• In triangle ABC, with a right angle at A and angle B measuring 45 degrees, one side length is 14√2 ft.
• The diagonal hypotenuse of triangular quilt pieces measures 18 in, leading to a side length of 9√2 in.

Trigonometric Values

• To find missing values using sine, sin = 8/15 results in an angle of approximately 32.23°.
• For cosine, cos = 9/20 yields a value of about 63.26°.

Application of Angles in Real Situations

• Viola drives 200 meters at a 9° incline, covering a horizontal distance of approximately 197.5 in.
• The distance to the top of a building measured from Mr. Collin's class is determined to be 154 ft.
• An airplane pilot observes an atoll at a 5° angle of depression; the horizontal distance to the atoll is 4,629 meters.

Height and Distance Calculations

• A surveyor measures 160 ft from a pole base and calculates the height to be approximately 307 ft using a 62° angle of elevation.
• The hypotenuse of a 30°-60°-90° triangle measuring 12 leads to a perimeter formula of 18 + 6√3.

Additional Measurements

• An unspecified measurement has been recorded as 27.8 in.
• Another angle measures 42°.
• One calculated distance is 454 miles.
• An angle related value is 48.6°.
• A final angle measurement found is 31°.