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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: 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: 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: 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: 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: 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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