Question

find the indicated side x. (use either the law of sines or the law of cosines, as appropriate. assume ∠b = 24° and ∠c = 96°. round your answer to one decimal place.) x =

Answer 1

The value of x in the figure is 1148.4

How the value of x is calculated.

∠A + ∠B +∠C = 180 (sum of int. angles of ∆)

24 + 96 +∠A = 180

120 + ∠A = 180

∠A = 180 - 120

∠A = 60⁰

Using sine rule

The sine rule relates the sides and angles of a triangle: a/sin A =b/sin B= c/sin C

where

a,b,c are sides of the triangle

A,B,C are interior angles facing the corresponding sides.

sinA/1000 = sinC/x

xsinA = 1000sinC

x = 1000sinC/sinA

x = 100sin96/sin60

x = 1000* 0.9945/0.8660

x = 994.5/0.8660

x = 1148.4

Complete question