Question on daughters 11th grade math. Cannot for the life of me figure it out.

Question

A kite needs to be flown at a height of 45 feet in the air the kites string is attached to a pole 5 feet off the ground. The angle of elevationwhere the kite is attached to the string is 45°. What is the length of rope that will hold the kite to correct height.

Answer 1

draw a vertical line representing the pole

draw a diagonal line slanted upwards to the right; this is the string whose length you want

draw a horizontal line to the right from the top of the pole

draw a horizontal line to the right from where the kite is attached to the striing

these two horizontal lines are parallel

draw a vertical line downwards to the ground from where the kite is attached to the string

this vertical line is 45 feet

the distance of this vertical line, when it cuts the bottom horizontal line, is 40 feet and the rest of the line is 5 feet, the same height as the 5 foot pole

the angle of elevation of the string at the top of the pole is also 45º because the two horizontal lines are parallel

you now have a right triangle with the string as the hypotenuse, the 40 foot vertical line as one leg and the horizontal distance from the top of the pole to the vertical line drawn downwards from where the kite attaches to the string

use the sine function

sin45º=40/x where x is the hypotenuse and thus the length of string needed

x=40/sin45º

x=40/0.70710678

x=56.56854259 feet, rounded to 56.6 feet because the answer is an approximation due to the value of sin45º, which is how long the string must be in order for the kite to be 45 feet above the ground

you could round up anywhere, for instance, 56.569 feet would be long enough