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.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl

(1, –1), (16, –4), (36, –6)

step-by-step explanation:

given that the function is

this can also be written as

we have to graph this function and check which list of points lie on the graph

see attachment for graph:

we find that the points lying are (1,-1) (16,-4) and (36,-6)

since square root is there we find that x can only be posiitve but y can be since square root both positive and negative.