Math  /  Geometry

QuestionUsing a ruler and a pair of compabses, construct a right-angled triangle with a base of 6 cm and a hypotenuse of 11 cm . You must show all of your construction lines.
Measure the angle opposite the base to the nearest degree.

Studdy Solution

STEP 1

1. We are constructing a right-angled triangle.
2. The base of the triangle is 6 cm.
3. The hypotenuse of the triangle is 11 cm.
4. We need to measure the angle opposite the base to the nearest degree.

STEP 2

1. Draw the base of the triangle.
2. Use a compass to draw the hypotenuse.
3. Complete the triangle by drawing the perpendicular line.
4. Measure the angle opposite the base.

STEP 3

Start by drawing a straight line segment using a ruler. This line segment will be the base of the triangle and should measure exactly 6 cm. Label the endpoints of this segment as points A A and B B .

STEP 4

Place the compass point on point A A and adjust the compass width to 11 cm, which is the length of the hypotenuse. Draw an arc above the line segment AB AB .

STEP 5

To create the right angle, we need to draw a perpendicular line from point B B . Use a set square or a compass to construct a perpendicular line to AB AB at point B B .

STEP 6

The intersection of the arc drawn in Step 2 and the perpendicular line from Step 3 will be point C C . This completes the right triangle ABC \triangle ABC with AB AB as the base and AC AC as the hypotenuse.

STEP 7

To measure the angle opposite the base AB AB , use a protractor. Place the protractor's center at point B B and align the base line of the protractor with line AB AB . Measure the angle ACB \angle ACB to the nearest degree.
The angle opposite the base is measured to be approximately 33 \boxed{33^\circ} .

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