Construct a right-angled triangle, given one side and one of the acute angles
1
Draw a rough sketch of the triangle to be constructed. Include the given information in your sketch.
A 3
Using a protractor, construct the acute angle given at A. Mark the point X, as shown. Draw a ray from A through X .
X X A Y 5
Mark the point where the rays [AX and [BY intersect asC. This is the required triangle.
A C A B X B C 2
14
Draw a line segment [AB] , which has a length equal to the given hypotenuse.
B 4 A B
Work out the other acute angle (remember, the three angles in a triangle add up to 180°). Using a protractor, construct this acute angle at B . Mark the point Y as shown. Draw a ray from B through Y .
Y
B
Discuss and discover
Working with a classmate, draw three different right-angled triangles. (i) Measure each of the angles. (ii) Measure each of the sides.
(iii) What have you discovered about the relationship between the size of each angle and its opposite side?
Practice questions 15·5 1. Construct the triangles using the rough sketches below:
(i) A (ii) A (iii) X (iv) 8 cm 8 cm 9 cm B 90° 5 cm C B 90° 4 cm C Z 90° 3 cm Y Section B Moving forward 247 9 cm O 90° M N 5 cm