Answer:
6. 36°
7. 33.1 cm
Explanation:
6. The tangent function relates the sides of a right triangle to the acute angles. Here, the angle west of south that is the direction of the ship from harbour is related to the distances by ...
tan(angle) = (18 km)/(25 km)
Then the angle can be found using the inverse tangent function:
angle = arctan(18/25) ≈ 35.75°
The direction back to the harbour is this same angle east of north. Since bearing angles are measured clockwise from north, the desired bearing is 36°.
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7. The cosine function relates the hypotenuse of a right triangle to the side adjacent to the angle of interest. Here, we have ...
cos(72°) = (diameter of glass)/(straw length to glass rim)
straw length to glass rim = (diameter of glass)/cos(72°) ≈ (9 cm)/0.309017
straw length to glass rim ≈ 29.1 cm
The straw extends 4 cm above the rim of the glass, so is 4 cm longer than this calculated value. The straw is about 33.1 cm long.