Answer:
To solve these types of problems, it's important to know trigonometric functions, especially tangent (tan), sine (sin) and cosine (cos).
sin = opposite side / hypotenuse
cos = adjacent side / hypotenuse
tan = opposite side / adjacent side
6. In this problem, let's first draw vertical line from the green downwards. This way we drew a right triangle. We know the angle at tee to be 15° and the line we just drew is opposite to this angle and is given to be 38 yards. The length from the tee to the green is actually hypotenuse of this triangle (let's mark it x). So, now we have:
sin = opposite side / hypotenuse
sin 15 = 38 / x
0.259 = 38 / x
x = 146.7 yards
7. We will again use a similar principle. We are given two sides of a right triangle; one opposite (8.5 m) and one adjacent (23.5 m) to the angle of elevation. That means that we can use tangent:
tan x = opposite side / adjacent side
tan x = 8.5 / 23.5
tan x = 0.3617
When we know the tan but not the angle, we use function arctan. So, the angle x equals:
x = arctan 0.3617
x = 19.9 or rounded x = 20°
8. Again, we have the right triangle, the angle (12°), the opposite side (4.25 feet) and we need to know the length of a ramp, which is hypotenuse to this triangle.
sin = opposite side / hypotenuse
sin 12 = 4.25 / x
0.208 = 4.25 / x
x = 20.4 feet
9. Hopefully, you can see the pattern. Again, the right triangle, the given angle (25°), opposite side (27 feet) and we need to find the adjacent side.
tan = opposite side / adjacent side
tan 25 = 27 / x
0.46 = 27 / x
x = 58 feet
10. Due to the congruent angles, angle of depression from the top of the tower to the ship is the same angle as the angle of elevation from ship to tower.
Again, we have the angle (20°), opposite side (135 meters) and we need to find the adjecent side.
tan = opposite side / adjacent side
tan 20 = 135 / x
0.36 = 135 / x
x = 375 meters.
Note that trigonometric function of an angle is something you find on the calculator and be sure to convert it to degrees not radiants.