Respuesta :

lucic

Answer:

sin 40/x =sin 60/12

Step-by-step 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

boffeemadrid

Answer:

The length of the pole is 9.90 feet.

Step-by-step 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

[tex]\frac{a}{sinA}=\frac{b}{sinB}=\frac{c}{sinC}[/tex]

Substituting the given values, we get

[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}=\frac{c}{sin80^{\circ}}[/tex]

Taking the first two equalities, we have

[tex]\frac{x}{sin40^{\circ}}=\frac{12}{sin60^{\circ}}[/tex]

[tex]x=\frac{12sin40^{\circ}}{sin60^{\circ}}[/tex]

[tex]x=\frac{12{\times}0.642}{0.866}[/tex]

[tex]x=8.90 feet[/tex]

Therefore, the length of the pole is 9.90 feet.

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