Question

in in the adjoining figure angle b is equal to 90 degree angle BAC is equal to 30 degree BC is equal to CD is equal to 4 cm and AD is equal to 10 cm find first sin theta and second cos theta​

Answer 1

here is ur ans dear hope it hlps u out

Answer 2

Given:

As in the diagram

To Find;

(i) sin θ

(ii) cos θ

Solution

Find the length AB:

$AB^2 + BD^2 = AD^2$

$AB^2 = AD^2 - BD^2$

$AB^2 = 10^2 - (4 + 4)^2$

$AB^2 = 100 - 64$

$AB^2 = 36$

$AB = 6$

Find the length AC:

$AB^2 + BC^2 = AC^2$

$AC^2 = 6^2 + 4^2$

$AC^2 = 36 + 16$

$AC^2 = 52$

$AC = 2\sqrt{13}$

Find sin θ:

$\sin \theta = \dfrac{\text{Opposite}}{\text{Hypotenuse}}$

$\sin \theta = \dfrac{4}{2\sqrt{13} }$

$\sin \theta = \dfrac{2\sqrt{13} }{13}$

Find cos θ:

$\cos \theta = \dfrac{\text{Adjacent}}{\text{Hypotenuse}}$

$\cos \theta = \dfrac{\text{6}}{2\sqrt{13} }$

$\cos \theta = \dfrac{3\sqrt{13} }{13}$