Calculate the size of the angle marked P in the right-angled triangle below. Draw the image of the triangle below under axial symmetry in the line k. Write down the length of the side opposite the angle R in the triangle shown. Opposite = Use the Theorem of Pythagoras to find the length of the hypotenuse of this triangle.

Junior Cycle Mathematics Geometry: Calculate the size of the angle

Calculate the size of the angle marked P in the right-angled triangle below - Junior Cycle Mathematics - Question 3 - 2015

Question 3

Calculate the size of the angle marked P in the right-angled triangle below. Draw the image of the triangle below under axial symmetry in the line k. Write down t... show full transcript

Worked Solution & Example Answer:Calculate the size of the angle marked P in the right-angled triangle below - Junior Cycle Mathematics - Question 3 - 2015

Step 1

Calculate the size of the angle marked P

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Answer

To find the angle P in the right-angled triangle, we use the fact that the sum of angles in a triangle is 180 degrees. Since this is a right-angled triangle, one angle is 90 degrees:

P + 22° + 90° = 180°

Solving for P gives:

P = 180° - 90° - 22° = 68°

Step 2

Draw the image of the triangle below under axial symmetry in the line k

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Answer

To draw the image of the triangle under axial symmetry in line k, replicate the triangle on the opposite side of line k, maintaining the same distance from the line. The reflected triangle will be a mirror image of the original.

Step 3

Write down the length of the side opposite the angle R in the triangle shown.

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Answer

The side opposite to the angle R is the one that is directly across from this angle. Given the triangle dimensions provided:

Opposite = 12 m.

Step 4

Use the Theorem of Pythagoras to find the length of the hypotenuse of this triangle.

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Answer

According to the Theorem of Pythagoras:

ext{Hypotenuse}^2 = ( ext{Opposite})^2 + ( ext{Adjacent})^2

For our triangle:

ext{Hypotenuse}^2 = 5^2 + 12^2 = 25 + 144 = 169

Taking the square root:

ext{Hypotenuse} = ext{√169} = 13 ext{ m}

Calculate the size of the angle marked P in the right-angled triangle below - Junior Cycle Mathematics - Question 3 - 2015

Worked Solution & Example Answer:Calculate the size of the angle marked P in the right-angled triangle below - Junior Cycle Mathematics - Question 3 - 2015

Calculate the size of the angle marked P

Draw the image of the triangle below under axial symmetry in the line k

Write down the length of the side opposite the angle R in the triangle shown.

Use the Theorem of Pythagoras to find the length of the hypotenuse of this triangle.

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