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Pipeng : Maths Trigonometry : Angles ALPHA Maths Homework Module

Angles ALPHA Maths Module

Description : Maths Trigonometry : Angles

Tools In This Module:

ALPHA : Trigonometry : Angles 01 : Acute Obtuse And Reflex Angles : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Angles 02 : Complementary Suplementary And Vertically Opposite Angles : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Angles 03 : Alternate Corresponding And Co-interior Angles On Parallel Lines : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Angles 04 : Interior Angles Of A Triangle : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Angles 05 : Angles In A Triangle With Two Sides Which Are Radii Of A Circle : ALPHA Maths Homework Exercise
ALPHA : Trigonometry : Angles 06 : Angles In A Triangle On A Semi Circle With One Side The Diameter Of The Circle : ALPHA Maths Homework Exercise


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Module List

ALPHA : Trigonometry : Angles 01 : Acute Obtuse And Reflex Angles : ALPHA Maths Homework Exercise

Description : Acute obtuse and reflex angles.

Discussion : Acute angles are less than 90 degrees. Obtuse angles are greater than 90 degrees and less than 180 degrees. Reflex angles are greater than 180 degrees and less than 360 degrees. See figure Types Of Angles

The homework exercise has 3 questions.

acute
obtuse
reflex

The equations are :

0 < acute < 90
90 < obtuse < 180
180 < reflex < 360

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ALPHA : Trigonometry : Angles 02 : Complementary Suplementary And Vertically Opposite Angles : ALPHA Maths Homework Exercise

Description : Complementary suplementary and vertically opposite angles.

Discussion : Complementary angles add to 180 degrees. Supplementary angles add up to 360 degrees. Vertically opposite angles are equal. See figure Types Of Angles

The homework exercise has 3 questions.

complementary
supplementary
vertically opposite

The equations are :

complementary angles add to 180
supplementary angles add to 360
vertically opposite angles are equal

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ALPHA : Trigonometry : Angles 03 : Alternate Corresponding And Co-interior Angles On Parallel Lines : ALPHA Maths Homework Exercise

Description : Alternate corresponding and co-interior angles on parallel lines.

Discussion : For parallel lines alternate angles are equal, corresponding angles are equal, and co-interior angles add up to 180 degrees. See figure Angles In Triangles And On Parallel Lines

The homework exercise has 3 questions.

alternate
corresponding
co-interior

The equations are :

alternate angles are equal
corresponding angles are equal
co-interior angles add to 180

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ALPHA : Trigonometry : Angles 04 : Interior Angles Of A Triangle : ALPHA Maths Homework Exercise

Description : Interior angles of a triangle.

Discussion : The interior angles of a triangle add to 180 degrees. The exterior angle equals the sum of the opposite interior angles. An isoceles triangle has two equal sides. See figure Angles In Triangles And On Parallel Lines

The homework exercise has 4 questions.

internal angle
exterior angle
opposite interior angle
isoceles triangle

The equations are :

A + B + C = 180
CX = A + B
for isoceles triangle A = B

where

A B C = interior angles of triangle
CX = exterior angle of apex C

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ALPHA : Trigonometry : Angles 05 : Angles In A Triangle With Two Sides Which Are Radii Of A Circle : ALPHA Maths Homework Exercise

Description : Triangle with two sides which are radii of a circle.

Discussion : A triangle formed with two radii of a circle is an isoceles triangle, with two equal sides and two equal angles. See Figure Angles On A Circle

The homework exercise has 3 questions.

angle C
angle A
side c

The equations are :

angle A = angle B
side a = side b
C = 180 - 2 A
a = 90 - C / 2
c = b sind(C) / sind(B)

Note : Angles are in degrees. Use the degree trig function sind().

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ALPHA : Trigonometry : Angles 06 : Angles In A Triangle On A Semi Circle With One Side The Diameter Of The Circle : ALPHA Maths Homework Exercise

Description : Triangle on a semi circle with one side the diameter of the circle.

Discussion : The opposite angle from the diameter (angle B) is a right angle. See Figure Angles On A Circle

The homework exercise has 3 questions.

angle C
angle A
side b

The equations are

B = 90
A = 90 - C
C = asind(a / b)
b = √(a2 + b2)

where

A B C = interior angles of triangle (B = 90)
a b c = sides of triangle (b = diameter)

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