Question

kim drew the diagram below to find x, the length of the pole holding up the stop sign that is at an angle with the ground as shown.

Answer 1

The length of the pole is 9.90 feet.

Explanation:

From the figure, it is given that x is the length of the pole and the pole casts a shadow when the sun is at 40 degree angle.

Thus, using the sine law, we have

`(a)/(sinA)=(b)/(sinB)=(c)/(sinC)`

Substituting the given values, we get

`(x)/(sin40^(\circ))=(12)/(sin60^(\circ))=(c)/(sin80^(\circ))`

Taking the first two equalities, we have

`(x)/(sin40^(\circ))=(12)/(sin60^(\circ))`

`x=(12sin40^(\circ))/(sin60^(\circ))`

`x=\frac{12{*}0.642}{0.866}`

`x=8.90 feet`

Therefore, the length of the pole is 9.90 feet.

Answer 2

sin 40/x =sin 60/12

Explanation:

The question is on law of sines

Given a triangle with sides a, b, c and angles A, B, C respectively, the sine law states that; a/sin A = b/sin B = c/sin C

In the question x=a, b=12 feet, A=40° , B=60° and C=80°

Finding value of x;

x/sin 40° = 12/sin 60°

x sin 60° =12 sin 40°

x=12 sin 40 / sin 60

x=29.33 ft