Question

The accompanying diagram shows a flagpole that stands on level ground. Two cables, r and s,

are attached to a pole at a point 20 feet above the ground. The combine length of the two cables
is 70 feet. If cable r is attached to the ground 8 feet from the base of the pole, what is the
measure of the angle, x, to the nearest degree, that cable s makes with the ground?

Answer 1

x =
`24^(o)`

Explanation:

r + s = 70 feet

Applying Pythagoras theorem to the triangle formed by cable r;

`/hyp/^(2)` =
`/adj1/^(2)` +
`/adj2/^(2)`

`/r/^(2)` =
`/20/^(2)` +
`/8/^(2)`

`r^(2)` = 400 + 64

= 464

r =
`√(464)`

= 21.541

Length of cable r is 21.54 feet.

So that,

r + s = 70 feet

21.54 feet + s = 70 feet

s = 70 feet - 21.54 feet

= 48.46 feet

Length of cable s is 48.46 feet.

Applying trigonometric function to the triangle formed by cable s, we have;

Sin θ =
`(opposite)/(hypotenuse)`

Sin x =
`(20)/(48.46)`

= 0.4127

x =
`Sin^(-1)` 0.4127

= 24.3746

x =
`24^(o)`

The measure of angle that s makes with the ground is approximately
`24^(o)`.