Download Trigonometry 1 - Trig Review

Math 20-2
Trigonometry: Lesson #1
Right-Angle Trigonometry: Review
Objective: By the end of this lesson you should be able to:
- Use the Pythagorean Theorem and trigonometric ratios to find missing sides and angles
in triangles.
Labeling Triangles

Vertices or angles –

Sides –

Hypotenuse –

Legs –
e.g. 1) Complete the labeling of this triangle.
A
b
Pythagorean Theorem
In a right-angled triangle:
e.g. 2) Determine the value of x for each of the following, to the nearest tenth.
a)
b)
x
9m
x
17.4 cm
13 m
5.5 cm
Math 20-2
Trigonometry: Lesson #1
Trigonometric Ratios:
When using trig ratios, sides are named in relation to a certain ______________.
In a right-angled triangle:
 sin A 

cos A 

tan A 
A
Trig ratios are used when:
 We are given a side and an angle and are looking for ____________________________.

We are given two sides and are looking for ______________________.
*** When solving trig ratios, make sure calculators are in ____________ mode.
Finding Unknown Sides (given one angle and a side)

Label the sides of the triangle in relation to _____________________________.

Select the appropriate trig ratio (using the side you are _____________ and the side you are
___________________________.)

Substitute in the values.

Solve for the unknown (cross multiply).
e.g. 3) Find the side x for the triangle shown. Round to the nearest tenth.
4 km
53
x
Math 20-2
Trigonometry: Lesson #1
Finding Unknown Angles (given two sides)

Label the triangle in relation to the angle _______________________________________.

Select the appropriate trig ratio (using the ________________ angle and the two __________
sides.)

Substitute in the values.

Solve for the unknown angle. (Use the _______ function on your calculator.)
e.g. 4) Solve the triangle below. (That means find all of the missing sides and angles.) Round
sides to the nearest tenth and angles to the nearest whole number.
K
9.7 cm
J
8.2 cm
L
Recall:
horizontal


Angle of Elevation –

Angle of Depression –
Both angle of elevation and depression are measured from the ___________________.
Math 20-2
Trigonometry: Lesson #1
e.g. 5) A submarine goes into a dive at an angle of depression of 33° and travels a total distance
of 275 m. Draw a diagram to illustrate the situation, and find how far beneath the surface
of the water the submarine is after its dive, to the nearest tenth of a metre.
Assignment:
Trigonometry Review Worksheet