Question

A factory has a smoke stack that is supported by a cable which attaches to it at point A and is secured to the ground at point G. The length of the cable is 165 feet. The distance from the base of the stack (point B) to point G is 120 feet. What is the angle the cable forms with the ground? Show your equation and state your answer to the nearest tenth of a degree.

Answer 1

Answer: 42.7 degrees

Explanation:

[asy]

unitsize(0.2 cm);

pair A, B, G;

A = (0,127);

B = (165,0);

G = (0,0);

draw(A--B);

draw(rightanglemark(G,A,B,4));

draw(rightanglemark(G,B,A,4));

label("A", A, N);

label("B", B, S);

label("G", G, SW);

label("165", (A + B)/2, NE);

label("120", (B + G)/2, W);

label("165", (A + G)/2, E);

draw(rightanglemark(B,A,G,12));

draw(B--G);

label("x", (B + G)/2, S);

[/asy]

We have a right triangle with hypotenuse 165 and leg 120. We want to find the angle opposite the 120 leg, which we will call x. We can use the sine function to solve for x:

sin(x) = 120 / 165

Taking the inverse sine of both sides, we get:

x = arcsin(120 / 165)

Evaluating this on a calculator, we get:

x = 42.7^\circ

Therefore, the cable forms an angle of 42.7 degrees with the ground.