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You are walking near a river. While standing at A, you measure an angle of 90° between B and C, as shown. You then walk to B and
measure
an angle of 61° between A and C. The distance between A and B is about 1 mile. How wide (in miles) is the river between A and C? Round your
answer to the nearest tenth.
61
B Im
A
The width is about
miles.
an angle of 61° between A and C. The distance between A and B is about 1 mile. How wide (in miles) is the river between A and C? Round your
answer to the nearest tenth.
61
B Im
A
The width is about
miles.
1 answer:
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Answer:
Step-by-step explanation:
Component form of a vector is given by , where
represents change in x-value and
represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector
, the magnitude is
.
190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being , one leg being
, and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.
In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.
Therefore, we have:
To find the other leg, , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:
Verify that
Therefore, the component form of this vector is