Oblique Triangles Part I Learning Goal: I can solve for a missing side or angle in a non-right triangle using sine law.

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Presentation transcript:

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 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 B C ⁰37⁰ 95⁰

Example 2 Solve the triangle (find all unknown values) Y X Z 21⁰ 17.9 cm 8.7 cm

Homework Sine Law: Pg # 3-6

Warm-Up: Sine Law Write sine law for the triangle below and select the appropriate rations to solve for ‘a’ a

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 # 4, 15-17

Homework Pg. 32 # 8, 10, 11, 15-17