Question 60 Answer and Explanation _ACT July 2020 Form C01 Math Section

60. A hill makes an angle of 20°with the horizontal,, as shown below. A taut guy wire, AB, extends from the base of the hill, point A, to point B on a vertical pole. Point B is 25 ft directly above where the pole is inserted into the ground at point C. Given that the length of AC is 60 ft, which of the following expressions represents the length, in feet, of the guy wire?

(Note: For a triangle with sides of length a, b, and c that are opposite angles ∠A, ∠B, and ∠C, respectively, $\dfrac{\sin \angle A}{a}$ = $\dfrac{\sin \angle B}{b}$ = $\dfrac{\sin \angle C}{C}$ and ${c}^{2}={a}^{2}+{b}^{2}$ - 2ab cos ∠C.)

F. $\frac{25\,sin\,{60}^{\circ}}{sin\,{20}^{\circ}}$

G. $\frac{25\,sin\,{70}^{\circ}}{sin\,{20}^{\circ}}$

H. $\frac{25\,sin\,{110}^{\circ}}{sin\,{20}^{\circ}}$

J. $\sqrt{{60}^{2}+{25}^{2}-2(60)(25)\,cos\,{70}^{\circ}}$

K. $\sqrt{{60}^{2}+{25}^{2}-2\left({60}\right)\left({25}\right)\cos{{110}^{\circ}}}$

Answer and Explanation

Your Answer is

Correct Answer is K

Explanation