Math1083Lab Worksheets 132 PDF

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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.

#1 label each angle as acute, obtuse, or right. 1. Acute angle 2. Right angle 3. Obtuse angle 4. Acute angle 5. Right angle 6. Obtuse angle

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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. O_____ b) A triangle with angles measured 30°, 50°, 100°, respectively. O_________ c) A triangle with angles measured 45°, 50°, 85°, respectively. O_________ d) A triangle with angles measured 20°, 70°, 90°, respectively. R_________

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. a) AB = 6, BC = 8, AC = 10 AB2+BC2=AC2 Therefore, 62+82=102 for a right angled triangle. Which is 100=100 and thus a right angled triangle. Angle A, cosA= adjacent/hypotenuse Cos A=6/10 Cos A=0.6 Angle A= Cos-10.6 A =53.130 Angle B is 900

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b) AB = 2, BC =

, AC = 4

AB2+BC2=AC2 Therefore, 22+3.52=42 for a right-angled triangle 4+12=16 It is a right-angled triangle Angle A=adjacent/hypotenuse 2/4=0.5 Cos-1=0.5 =60Ɵ Angle B=90Ɵ

c) c) AB = 2, BC = 3, AC = 5 AB2+BC2=AC2 Therefore, 22+32=√13=3.6 It is not a right-angled triangle

d) AB = 5, BC = 5, AC = 5 AB2 +BC 2 =AC2 52+52=50

e) AB

= , BC = , AC = all sides are equal and thus not a right Angled triangle.

It is a right-angled triangle Angle A=5/5√2 =0.7071 34

Cos-1 0.7071=450 Angle B is 900

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 5+4=9 and thus 9 is greater than 7, which means 7,5, and 4 can make a triangle. b) 3,6,2 3+2=5, and thus 5 is less than 6, which means that 3,6, and 2 cannot make a triangle. c) 5,2,4 2+4=6, and thus 6 is greater than 5, which means 5,2, and 4 can make a triangle. d) 8,2,8 8+2=10, which is greater than 8, and thus 8,2,8 can make a triangle. e) 9,6,5 6+5=11, which is greater than 9, and therefore, 9,6,5 can make a triangle. f) 5,8,3 5+3=8, making the sum of small sides to be equal to the length of the longest side, meaning 5,8, and 3 cannot make a triangle.

#5. Solve each equation for � a)

3

= sin 30°

�

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3/x=sin300 x=3/sin300 =3/0.5 x=6 b)

2

= x

½

0.7

x=4(0.7) x =2.8

Area of a triangle

ℎ∙ ℎ ℎℎ

#6. Find the area of the triangle. a)

b)

Area = ½ x b x h ½ x 12 x 4 = 24

52 – 32 = h2 h=4 ½ x 10 x 4 = 20 ½ x 3 x 3 = 14 20 – 6 = 14

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