Question

find the area of triangles ABC in which angle B =60degree, angleC =90degree, AB=20cm and AC = 5cm​

Answer 1

[NOTE : refer the given figure in the attachment ]

Answer

Area of triangle ABC is

$\boxed{\textbf{\large{Area= 48.375 cmsquare }}}$

Given

IN a given triangle ABC,

⚫angle ACB = 90 degree

⚫angle ABC =60 degree

⚫side AB = 20 cm

⚫side AC =5 cm

Explanation

As a given,

In a triangle ABC

angle ACB=90 degree

therefor it is a right angle triangle

⚫

therefor by Pythagoras theorem

(hypotenuse )^2 =

=(1st side)^2 +(2nd side) ^2

(AB) ^2 =(AC) ^2 + (BC) ^2

[side opposite to 90 degree angle is hypotenuse, so the side AB Is a hypotenuse ]

(20)^2 = (5)^2 + (BC) ^2

400 = 25 + (BC) ^2

400-25 = (BC) ^2

(√375)= BC

19.35 = BC

$\boxed{\textbf{\large{sideBC=19.35cm}}}$

Therefor,

In a triangle ABC,

base = sideBC=19.35cm

height=sideAC=5cm

Area of triangle =

Area of triangle = =1/2 X base X height

=1/2 X 19.35 X 5

= 2.5 x 19.35

=48.375 cm^2

therefor the Area of triangle ABC is

$\boxed{\textbf{\large{Area= 48.375 cmsquare }}}$