A world in disarray sparknotes

Math 1083 Worksheet 13 Getting Ready for Non-Right Triangles: Law of Sines

Objectives: 1. Distinguish right triangles and non-right triangles

2. Apply the Pythagorean theorem

3. Review the rule for side lengths of a triangle

4. Review the area formula for a triangle

Review: A right angle is an angle of 90°, as in a corner of a square. An acute angle is an angle that measures less than 90 but more than 0. An obtuse angle is an angle that measures more than 90 but less than180.

#1. Label each angle as acute, obtuse, or right.

Recall: A right triangle is a triangle in which one angle is a right angle. A triangle that is not a right triangle is an oblique triangle. #2. Determine whether each triangle is a right triangle or an oblique triangle. Write “R” for right triangles and “O” for oblique triangles.

a) An equilateral triangle. ___________

b) A triangle with angles measured 30°, 50°, 100°, respectively. _________

c) A triangle with angles measured 45°, 50°, 85°, respectively. _________

d) A triangle with angles measured 20°, 70°, 90°, respectively. _________

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Pythagorean Theorem and Its Converse Pythagorean Theorem: For any right triangle, a2 + b2 = c2, c is the length of the hypotenuse. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

Converse of the Pythagorean Theorem For any triangle, if a2 + b2 = c2, then a, b, c are the lengths of a right triangle and c is the hypotenuse.

# 3 Given triangle ABC below (The picture is not drawn to scale). For each problem, determine

whether it is a right triangle. Find angle A and B if possible.

b) AB = 2, BC = 2√3, AC = 4

d) AB = 5, BC = 5, AC = 5√2

a) AB = 6, BC = 8, AC = 10

c) AB = 2, BC = 3, AC = 5

e) AB = √5, BC = √5, AC = √5

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Rule for side lengths of a triangle If the sum of two shorter (smaller) lengths is greater than the longest length, then they can form a triangle.

#4 Determine if the three numbers can be the measures of the sides of a triangle. Explain.

a) 7, 5, 4 b) 3, 6, 2 c) 5, 2, 4 d) 8, 2, 8 e) 9, 6, 5 f) 5, 8, 3

#5. Solve each equation for 𝑥

a) 3

𝑥 = sin 30° b)

2 1

2

= 𝑥

0.7

Area of a triangle = 1

2 ∙ 𝑏𝑎𝑠𝑒 ∙ ℎ𝑒𝑖𝑔ℎ𝑡

#6. Find the area of the triangle.

a) b)