In the given figure, △ABC is right angled at B. If AC = 20 cm and tan A = , find the lengths of AB and BC.

tan A = Given, tan A = Let BC = 3x and AB = 4x. Now by pythagoras theorem AC2 = BC2 + AB2 (20)2 = (3x)2 + (4x)2 400 = 9x2 + 16x2 25x2 = 400 x2 = 16 x = = 4 AB = 4x = 16 cm and BC = 3x = 12 cm. Hence, length of AB = 16 cm and BC = 12 cm.

Mathematics

In the given figure, △ABC is right angled at B.
If AC = 20 cm and tan A = $\dfrac{3}{4}$ , find the lengths of AB and BC.

Trigonometrical Ratios

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Answer

tan A = $\dfrac{\text{perpendicular}}{\text{base}} = \dfrac{BC}{AB}$

Given,

tan A = $\dfrac{3}{4}$

Let BC = 3x and AB = 4x.

Now by pythagoras theorem

AC² = BC² + AB²

(20)² = (3x)² + (4x)²

400 = 9x² + 16x²

25x² = 400

x² = 16

x = $\sqrt{16}$ = 4

AB = 4x = 16 cm and BC = 3x = 12 cm.

Hence, length of AB = 16 cm and BC = 12 cm.

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Mathematics

In the given figure, △ABC is right angled at B.
If AC = 20 cm and tan A = $\dfrac{3}{4}$ , find the lengths of AB and BC.

Trigonometrical Ratios

Answer

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In the given figure, △ABC is right angled at B.
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If (cos θ + sec θ ) = $\dfrac{5}{2}$ , find the value of (cos²θ + sec²θ).

If cos θ = $\dfrac{2x}{1 + x^2}$ , find the values of sin θ and tan θ in terms of x.

Without using trigonometric table, find the values of:
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(ii) sin 45° cos 30° - cos 45° sin 30°
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(iv) cos 90° + cos² 45° sin 30° tan 45°