Question

GEOMETRY.INCLUDE CLEAR ANSWER PLEASE. AS WELL AS EXPLANATION

Answer 1

Here are 2 ways of solving this problem.

1) The angle the triangle's vertical leg makes with the dotted line is 90 degrees.

90 - 28 = 62

The triangle's left upper angle is 62 degrees.

For the 62-deg angle, 350 ft is the adjacent leg.

The hypotenuse is x.

The trig ratio that relates the adjacent leg to the hypotenuse is the cosine.

`\cos \theta = (adj)/(hyp)`

`\cos 62^\circ = (350~ft)/(x)`

`x \cos 62^\circ = 350~ft`

`x = (350~ft)/(\cos 62^\circ)`

`x = 745.51906...`

Answer x = 745.5 ft

2) The dotted line has an arrow head. The triangle's horizontal leg also has an arrowhead. That means that the horizontal leg of the triangle and the dotted line are parallel. By alternate interior angles, the lower right angle of the triangle is also 20 deg.

For the 28-deg angle, the 350 ft leg is the opposite leg.

The hypotenuse is x.

The trig ratio that relates the opposite leg to the hypotenuse is the sine.

`\sin \theta = (opp)/(hyp)`

`\sin 28^\circ = (350~ft)/(x)`

`x \sin 28^\circ = 350~ft`

`x = (350~ft)/(\sin 28^\circ)`

`x = 745.51906...`

Answer x = 745.5 ft

As you can see, both methods give the same answer.

Answer 2

the answer I got is x=1132.6

You have to find the degrees inside of the triangle. Since the top and bottom horizontal lines are parallel, then 28° and the other angle next to it are complementary(90°).

That angle is 62°, then the 90°, and a triangle, so the last measurement is 18°, totalling to 180.

You have to find the hypotenuse, so I chose the angle 18° to use. the equation I got was sin18=350/x
(sin is opposite side over hypotenuse)

I multiplied the x to the other side, and divided the sin18 to the other side. now you have x=350/sin18.

plug that into the calculator, and you get the above answer.