Someone must have beaten me here. Devora thinks, dismayed by the empty treasure chest. Then, just as she's about to close the lid, she notices a map (shown below).

"Curse these trig-loving pirates!" Devora mutters as she looks at the map. Then, after thinking for a moment, she walks back to the entrance of the secret cave, measuring 484848 meters along the way. After performing a calculation, Devora walks back to the empty treasure, faces the entrance, and turns a certain number of degrees to her left before walking 898989 meters to the treasure.

Supposing that the angle at the Cave entrance is acute and that Devora's calculations were correct, how many degrees did she turn?

she turned 82 degrees.

Step-by-step explanation:

Suppose, the unknown angle is A

Now, we know that according to the sine law ,

the ratio of side of a triangle and the sine value of the angle opposite to that side is same . It says that,

if a triangle has 3 sides a,b and c and 3 angles A,B,and C and they are opposite to the sides respectively then,

a/SinA=b/sinB=c/SinC

check the image below in attachment.

From the diagram at attachment.

here , angle A is required.

given, angle C= 30

side b=89 m and c= 48 m

sin law says a/sinA=b/sinB=c/sinC

first we take , b/sinB=c/sinC

or, 89/sinB= 48/sin30

or, sinB=( 89×0.5)/48 =0.92

or, B=68

we know, in every triangle , the sum of 3 angles of a triangle is 180

then, A+B+C=180

or, A=180-B-C= 180 - ( B+C)

=180-(68+30)

or, A = 82

therefore , the required angle is 82 degree.

she turned 82 degrees.