Question

the area of the triangle is 480 cm square if two of its side are 48 cm and 52 cm find the third side​

Answer 1

Answer:

The area of a triangle is given by (ab/2)sin C. Here

(52*48/2) sin C = 480, or

sin C = 2*480/(52*48) = 0.384615384 or <C = arcsin 0.384615384 = 22.61986495 deg.

Applying cosine formula we get the third side as c^2= a^2+b^2–2a*b*cos C

= 52^2+48^2–2*52*48*cos 22.61986495 = 2704+2304-4608 = 400. Hence

c = 20 cm.

Check: 2s = 52+48+20 = 120, or s = 60.

Area by Heron’s formula = [60(60–52)(60–48)(60–20)]^0.5

= [60*8*12*40]^0.5 = 480. Correct.

The third side is 20 cm.

Explanation:

hope you are understood