Download UNIT 7 – TRIGONOMETRY IN ACUTE TRIANGLES (Lesson 1

UNIT 7 – TRIGONOMETRY IN ACUTE TRIANGLES
(Lesson 1 – Sine Law)
When working with right triangles we use the three trigonometric ratios to determine unknown
SOH CAH TOA
sides and angles.
What about non-right triangles? There is no hypotenuse
A) Definition
An oblique triangle is a triangle that is not right-angled.
A triangle that is not right-angled is either an acute triangle (all angles less than 90˚)or an
obtuse triangle (one angle greater than 90˚).
The sine law may be used to solve oblique triangles.
The
TheSine
SineLaw
Law
𝑠𝑖𝑛𝐴
𝑠𝑖𝑛𝐶
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐵
== 𝑠𝑖𝑛𝐵== 𝑠𝑖𝑛𝐶
𝑎𝑎
𝑏𝑏
𝑐𝑐
A
𝑎𝑎
𝑏
𝑐
== 𝑏 == 𝑐
𝑠𝑖𝑛𝐴
𝑠𝑖𝑛𝐴 𝑠𝑖𝑛𝐵
𝑠𝑖𝑛𝐵 𝑠𝑖𝑛𝐶
𝑠𝑖𝑛𝐶
OR
OR
B
**Only 2 parts of the Sine Law are used at a time.
B) Case 1 – Given Two Angles and a Side.
Example 1: Solve the triangle.
C
80°
A
30°
38 m
B
C) Case 2 – Given Two Sides and an Opposite Angle.
Example 2: Solve the triangle.
A
6 cm
28°
B
12 cm
C
C
D) Word Problem
Example 3: A field is in the shape of a triangle. Side a has length 620 m, the measure of ∠𝐴
is 56 , and the measure of ∠𝐵 is 62 . Calculate the perimeter of the field, correct
to the nearest tenth.
The Sine Law can be used to find:
An unknown angle if two sides and
An unknown side if two angles and
a side are known.
the angle opposite one of the
known sides are known