Transcript Lesson_5 Sine Law

Oblique Triangles
Part I
Learning Goal: I can solve for a missing side
or angle in a non-right triangle using sine law
Oblique Triangle
• An oblique triangle is any non right triangle
• May be acute (all angles less than 90⁰) or obtuse (one angle
greater than 90⁰)
– Acute triangles may be equilateral or isosceles
– Obtuse triangles may also be isosceles
Equilateral: All sides
and angles are equal
Isosceles: 2 angles (and
opposite sides) are equal
Sine Law
• Sine Law can be used to solve for unknown sides or
angles in an oblique triangle when a matching sideangle pair is known
Even though
there are three
terms in the
equation, we only
ever use two at
once
Example 1
• Label each side of the
triangle with the correct
letter (a, b, c)
• Write the sine law for the
triangle shown and circle
the ratios you would use
• Use the information
provided to solve for side b
A
95⁰
7.2
B
37⁰
48⁰
C
Example 2
Y
Solve the triangle (find all unknown values)
21⁰
17.9 cm
X
8.7 cm
Z
Oblique Triangles
Applications of Sine Law
Learning Goal: I can apply sine law to solve
problems based on realistic situations
Example 1
A tent is being constructed for an outdoor wedding. If
the tent is 11 m wide and the two identical support
beams for the roof need to meet at an angle of 70,
how long do the support beams need to be?
Example 2
A plane flies between two tracking towers located 25
km apart. From station 1, the angle of elevation to the
plane is 46 and from the second tower is 68. To one
decimal place, what is the altitude of the plane?
Homework
• Pg. 31-32 # 4, 15-17