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Constructions Exercise 17.5

Question: 1

Draw a right triangle with hypotenuse of length 5 cm and one side of length 4 cm.

Solution:

Constructions Exercise 17.5 Question: 1

Steps of construction:

  • Draw a line segment QR = 4 cm.

  • Draw ∠QRX of measure 90°.

  • With centre Q and radius PQ = 5 cm, draw an arc of the circle to intersect ray RX at P.

  • Join PQ to obtain the desired triangle PQR.

PQR is the required triangle.

 

Question: 2

Draw a right triangle whose hypotenuse is of length 4 cm and one side is of length 2.5 cm.

Solution:

Constructions Exercise 17.5 Question: 2

Steps of construction:

  • Draw a line segment QR = 2.5 cm.

  • Draw ∠QRX of measure 90°.

  • With centre Q and radius PQ = 4 cm, draw an arc of the circle to intersect ray RX at P.

  • Join PQ to obtain the desired triangle PQR.

PQR is the required triangle.

 

Question: 3

Draw a right triangle having hypotenuse of length 5.4 cm, and one of the acute angles of measure 30° 

Solution:

Constructions Exercise 17.5 Question: 3

Let ABC be the right triangle at A such that hypotenuse BC = 5.4 cm. Let cC = 30°.

Therefore ∠A + ∠B + ∠C = 180°∠B = 180°− 30°− 90° = 60°

Steps of construction:

  • Draw a line segment BC = 5.4 cm.

  • Draw angle CBY = 60°

  • Draw angle BCX of measure 30° with X on the same side of BC as Y.

  • Let BY and CX intersect at A.

Then ABC is the required triangle.

 

Question: 4

Construct a right triangle ABC in which AB = 5.8 cm, BC = 4.5 cm and ∠C = 90°.

Solution:

Constructions Exercise 17.5 Question: 4

Steps of construction:

  • Draw a line segment BC = 4.5 cm.

  • Draw ∠BCX of measure 90°..

  • With centre B and radius AB = 5.8 cm, draw an arc of the circle to intersect ray BX at A.

  • Join AB to obtain the desired triangle ABC.

ABC is the required triangle.
 

Question: 5

Construct a right triangle, right angled at C in which AB = 5.2 cm and BC= 4.6 cm.

Solution:

Constructions Exercise 17.5 Question: 5

Steps of construction:

  • Draw a line segment BC = 4.6 cm.

  • Draw ∠BCX of measure 90°

  • With centre B and radius AB = 5.2 cm, draw an arc of the circle to intersect ray CX at A.

  • Join AB to obtain the desired triangle ABC.

ABC is the required triangle.


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