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

1 Like

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.

Answered By

3 Likes

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

Related Questions

If (cos θ + sec θ ) = $\dfrac{5}{2}$ , find the value of (cos²θ + sec²θ).

Evaluate x and y from the given figure.

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:
(i) sin 60° cos 30° + cos 60° sin 30°
(ii) sin 45° cos 30° - cos 45° sin 30°
(iii) cos 60° cos 45° + sin 60° sin 45°
(iv) cos 90° + cos² 45° sin 30° tan 45°

Mathematics

In the given figure, △ABC is right angled at B.If AC = 20 cm and tan A = 34\dfrac{3}{4}43​, find the lengths of AB and BC.

Trigonometrical Ratios

Answer

Related Questions

If (cos θ + sec θ ) = 52\dfrac{5}{2}25​, find the value of (cos2θ + sec2θ).

Evaluate x and y from the given figure.

If cos θ = 2x1+x2\dfrac{2x}{1 + x^2}1+x22x​, find the values of sin θ and tan θ in terms of x.

Without using trigonometric table, find the values of:(i) sin 60° cos 30° + cos 60° sin 30°(ii) sin 45° cos 30° - cos 45° sin 30°(iii) cos 60° cos 45° + sin 60° sin 45°(iv) cos 90° + cos2 45° sin 30° tan 45°

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.

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:
(i) sin 60° cos 30° + cos 60° sin 30°
(ii) sin 45° cos 30° - cos 45° sin 30°
(iii) cos 60° cos 45° + sin 60° sin 45°
(iv) cos 90° + cos² 45° sin 30° tan 45°