Investigation: Right Triangle Trigonometry

Part 1: Pythagorean Theorem

What is the Pythagorean Theorem and when is it used?

Using the equation above (Pythagorean Theorem), find the missing lengths of this triangle.

a) b)

Part 2: Trigonometric Ratios

What are trigonometric ratios and when are they used?

SOHCAHTOA: Sine, Cosine, and Tangent Ratios

1) Find the following trigonometric ratios.

a) b) c)

d) e) f)

2) Find the missing lengths using trigonometric ratios.

a) b) c)

d) e) f)

Part 3: Trigonmetric Inverses

When do we use trigonometric inverses?

Example:

Find the missing angle using trigonometric inverses.

a) b)

c) d)

e) f)

Part 4: Word Problems1) A surveyor is standing 115 feet from the base of the Washington Monument. The surveyor measures the angle of elevation to the top of the monument as 78.3°. How tall is the Washington Monument?

2) The angle of from the top of the castle to boat is 25°. If theboat is 50 m from the base of the castle, how high is the castle?

3) A helicopter is hovering above a road at an altitude of 24 m. At a certain time, thedistance between the helicopter and a car on the road is 45.0 m. Calculate the angle from the car to the helicopter.

24 m

45 m