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

Junior Cycle Mathematics Trigonometry: 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

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 th... 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

Step 1

Calculate the size of the angle marked P in the right-angled triangle below.

96%

114 rated

Answer

To find the size of the angle P in the right-angled triangle, we use the property that the sum of angles in a triangle is 180 degrees. The triangle has one right angle (90 degrees) and the given angle of 22 degrees. Therefore, we can calculate angle P as follows:

$P = 180^ ext{°} - 90^ ext{°} - 22^ ext{°} = 68^ ext{°}$

Step 2

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

99%

104 rated

Answer

To draw the triangle under axial symmetry along line k, mirror the right-angled triangle. The left side of the triangle will now appear on the right side of line k, maintaining the same orientation and angle measurements.

Step 3

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

96%

101 rated

Answer

The length of the side opposite the angle R is given as:

Opposite = 12 m.

Step 4

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

98%

120 rated

Answer

To find the hypotenuse (h) using the Theorem of Pythagoras, we use the formula:

$h = \\sqrt{a^2 + b^2}$ where:

a = 5 m (one side of the triangle)
b = 12 m (the other side)

Thus,

$h = \\sqrt{5^2 + 12^2} = \\sqrt{25 + 144} = \\sqrt{169} = 13 m$ .

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

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

Join the Junior Cycle students using SimpleStudy...