Question

in triangle abc angle C is equals to 90 degree angle a equals to 45 degree and ab = 10 CM using trigonometric ratios find the length of BC

Answer 1

so the other angle will be 45 degree as sum of angle of triangle is 180

Answer 2

Given :

In triangle abc angle C is equals to 90 degree angle a equals to 45 degree and ab = 10 CM

To Find:

Find the length of BC

Solution:

Refer the attached figure

In triangle ABC

$\angle A = 45^{\circ}\\\angle C = 90^{\circ}$

Angles sum property of triangle : The sum of all angles of triangle is 180°

$\angle A+ \angle B + \angle C = 180^{\circ}\\45+\angle B + 90 = 180\\\angle B = 180-(90+45)\\\angle B = 45^{\circ}$

AB = Hypotenuse = 10 cm

$Cos \theta = \frac{Base}{Hypotenuse}\\Cos 45^{\circ}=\frac{BC}{AB}\\\frac{1}{\sqrt{2}}=\frac{BC}{10}\\\frac{1}{\sqrt{2}} \times 10=BC$

7.07=BC

Hence The length of BC is 7.07 cm