Question

construct a right angled triangle having hypotenuse 7 cm and one of its acute angles measuring 45°.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Constructed a right-angled triangle  △ABC  with AB= 7cm, ∠A= 45°, ∠B=45°, and ∠C=90°

Given,

Hypotenuse of a right-angled triangle = 7cm

where one of its acute angles measures = 45°

To find,

To construct a right-angled triangle having a hypotenuse of 7 cm and one of its acute angles measuring 45°.

Solution,

Steps to construct a right-angle triangle whose hypotenuse and an angle are given below:

1. Draw a line AB of 7cm

Here, AB is the hypotenuse.

Hence Let ∠C=90°

2. Take B as a center, draw an angle of ∠B=45° with a ruler and compass

We know that

According to the angle sum property of the triangle, ∠A+∠B+∠C=180°

∠A + 45° + 90° = 180°

∠A + 135° = 180°

∠A=180° - 135°

∠A= 45°

4. Take A as a center, and draw an angle of ∠A = 45° with a ruler and compass.

5. Join the respective angle lines to meet each other at point B.

Thus, △ABC is the required triangle with AB= 7cm, ∠A= 45°, ∠B=45°, and ∠C=90°

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