Can someone help me with this math? d**n its pissing me off?

Question

12. A support cable for a 64 foot tower forms a 70° angle with the ground. What is the length of the cable to the nearest foot?

a. 21 ft

b. 32 ft

c. 60 ft

d. 68 ft

13. If the angle of elevation of the sun with the ground is 10°, what is the length of a shadow cast by a six-foot person to the nearest foot?

a. 12 ft

b. 20 ft

c. 34 ft

d. 40 ft

14. A kite on a 250 foot string makes a 58° angle with the ground. What is the height of the kite above the ground to the nearest foot?

a. 176 ft

b. 185 ft

c. 198 ft

d. 212 ft

15. A 12 foot ladder is leaning against a wall. If the ladder reaches 8 feet high on the wall, what is the angle the ladder forms with the ground to the nearest degree?

a. 36°

b. 42°

c. 48°

d. 54°

Answer 1

For these problems, a picture is worth a thousand words,

and drawing pictures here is near impossible, so we'll have to make do.

12: Right triangle: looking for hypotenuse,

have angle and opposite side.

Ratio of opposite site to hypotenuse  = sin (angle)

64 / hyp = sin(70°)

hyp = 64 / sin(70°)

13: This time the shadow is the adjacent side,

so we use the tangent.

6 / shadow = tan(10°)

14: Same as problem 12, but this time

we are given the hypotenuse and have to find the opposite side.

opp / hyp = sin(58°)

opp = 250 sin(58°)

15: Now we need to find the angle

hyp = 12, opp side = 8

sin (x°) = 8/12 = 2/3

So we want sin^-1(2/3) or arcsin (2/3)