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In δAbc is a Right Triangle Such that ∠C = 90° ∠A = 45°, Bc = 7 Units Find ∠B, Ab and Ac - CBSE Class 10 - Mathematics

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Question

In ΔABC is a right triangle such that ∠C = 90° ∠A = 45°, BC = 7 units find ∠B, AB and AC

Solution

Sum of angles in Δle = 180°

∠A + ∠B + ∠C = 180°

45° + ∠B + 90° = 180°

∠B = 180° − 135°

∠B = 45°

From figure `cos B = (BC)/(AB)`

`cos 45^2 =  7/(AB)`

`1/sqrt2 .  7/(AB)`

`AB = 7sqrt2 units`

From figure `sin B = (AC)/(AB)`

`sin 45^@ = (AB)/(7sqrt2)`

`1/sqrt2 = (AC)/(7sqrt2)`

∴ AC =  7 units

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Solution In δAbc is a Right Triangle Such that ∠C = 90° ∠A = 45°, Bc = 7 Units Find ∠B, Ab and Ac Concept: Trigonometric Ratios.
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