Find the value of x in the triangle shown below.

Step-by-step explanation:

Use the Pythagorean theorem which states that in every right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs. So, if in a right triangle there are legs of length a and b, and the measure of the hypotenuse is c, then the following relationship is true:

In this case, let:

Hence:

Solving for x:

Therefore, the value of x in the triangle is 8

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,