Oblique TrianglesPart 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 side-angle 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

BC

7.2

48⁰37⁰

95⁰

Example 2Solve the triangle (find all unknown values) Y

X Z

21⁰

17.9 cm

8.7 cm

Oblique TrianglesApplications of Sine Law

Learning Goal: I can apply sine law to solve problems based on realistic situations

Example 1A 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 2A 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