Question

From the information in the figure, complete the following activity to find the length of the hypotenuse AC

Answer 1

Length of the hypotenuse = 16 cm and

Blanks are 180°, 30° and AC = 16 cm.

Given:
From the given figure,

ABC is a right-angled triangle and BC = 8 cm

To find:

Find the length of AC and fill in the blanks

Solution:  

As we know the sum of angles in a triangle is 180°

=> ∠A + ∠B + ∠C = 180°

=> ∠A + 90° + 60° = 180°      [ ∵ ∠C = 60° and ∠B = 90° ]  

=> ∠A = 180° - 150°

=> ∠A = 30°

As we know in a right-angle triangle,

sin = opposite side/hypotenuse

From the given triangle,

=> sin A = BC/AC

=> BC = sin A × AC

=> sin 30° =  8/AC

=>  1/2 = 8/AC                [ Since sin 30° = 1/2 ]

=> 1 × AC = 2 × 8            [ Do cross multiplication ]

=>  AC = 16 cm

Therefore,

Length of the hypotenuse = 16 cm and

Blanks are 180°, 30° and AC = 16 cm

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