Question

construct a right angled triangle ABC in which AB=6 cm, angle B = 90° and angle C =30°

Answer 1

Answer:

Step-by-step explanation:

1. take ab as base. Now make 90 degree angle at point B. and then  draw the line through 90 degree. Now take a certain point C at BC(line u just made) and now draw the ling BA from point B. Easy.

Answer 2

Answer:

Step-by-step explanation:

• Consider the following situation. If a circle is drawn through B, D, and C, BC will be its diameter as ∠BDC  is of measure 90∘
• The center E of this circle will be the mid-point of BC.

The required tangents can be constructed on the given circle as follows.

Step 1

Join AE and bisect it. Let F be the mid-point of AE.

Step 2

Taking F as centre and FE as its radius, draw a circle which will intersect the circle at point B and G. Join AG.

AB and AG are the required tangents.

∠AGE is an angle in the semi-circle. We know that an angle in a semi-circle is a right angle.

∴∠AGE=90∘

⇒EG⊥AG

Since EG is the radius of the circle, AG has to be a tangent of the circle.

Already,

∠B=90∘

⇒AB⊥BE

Since BE is the radius of the circle, AB has to be a tangent of the circle.

Justification

The construction can be justified by proving that AG and AB are the tangents to the circle. For this, join EG.

∠AGE is an angle in the semi-circle. We know that an angle in a semi-circle is a right angle.

∴∠AGE=90∘

⇒EG⊥AG

Since EG is the radius of the circle, AG has to be a tangent of the circle.

Already,

∠B=90∘

⇒AB⊥BE

Since BE is the radius of the circle, AB has to be a tangent of the circle.