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The triangle BOP has: one side that is 8 cm long one angle of 40° one angle of 60° - Junior Cycle Mathematics - Question 6 - 2016
Question 6
The triangle BOP has: one side that is 8 cm long one angle of 40° one angle of 60°. (a) Work out the size of the third angle in the triangle BOP. (b) Draw a sketch... show full transcript
Worked Solution & Example Answer:The triangle BOP has: one side that is 8 cm long one angle of 40° one angle of 60° - Junior Cycle Mathematics - Question 6 - 2016
Step 1
Work out the size of the third angle in the triangle BOP.
Answer
To find the third angle in triangle BOP, we can use the fact that the sum of the angles in a triangle is always 180°.
Let the angles be:
- Angle B = 40°
- Angle O = 60°
- Angle P = x
Using the equation:
x = 180° - (40° + 60°) = 180° - 100° = 80°
Thus, the third angle P is 80°.
Step 2
Draw a sketch of one such triangle BOP.
Answer
To sketch the triangle BOP:
- Start by drawing a horizontal line segment of length 8 cm to represent side OP.
- At point O, construct an angle of 40° using a protractor.
- At point P, construct an angle of 60°.
- Connect points B, O, and P to form triangle BOP.
On the sketch, label:
- Angle B as 40°
- Angle O as 60°
- Angle P as 80°
- Side OP as 8 cm.
Step 3
Construct the triangle BOP from your sketch.
Answer
To accurately construct triangle BOP:
- Make sure to use a ruler to draw the base OP measuring 8 cm.
- Use a compass to set the angle at point O to 40° and draw a line extending from O.
- Set the angle at point P to 60° in a similar manner.
- Mark the intersection of the two lines to find point B.
- Finally, connect points B, O, and P to complete the triangle BOP.