Rosa is building a guitar. The second fret is 33.641\,\text{mm}33.641mm from the first fret. The third fret is 31.749\,\text{mm}
1 answer:
Answer:
65.39 mm.
Step-by-step explanation:
We have been given that Rosa is building a guitar. The second fret is 33.641 mm from the first fret. The third fret is 31.749 mm from the second fret.
We can find the distance between third fret and first fret by adding the distances between first fret to second fret and second fret to third fret.
Therefore, 3rd fret is 65.39 mm away from 1st fret.
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By using trigonometric relations, we will see that:
AC = 15.6 in
AB = 8.4 in.
<h3>How to get the measures of the other two sides of the right triangle?</h3>Here we have the right triangle where:
B = 90°
C = 40°
BC = 10 in.
Notice that is the adjacent cathetus to the angle C, then we can use the two relations:
- sin(a) = (adjacent cathetus)/(hypotenuse).
- tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
- hypotenuse = AC
- opposite cathetus = AB.
Then we will have:
sin(40°) = 10in/AC.
AC = 10in/sin(40°) = 15.6 in
tan(40°) = AB/10in
tan(40°)*10in = AB = 8.4 in.
So we can conclude that for the given right triangle we have:
AC = 15.6 in
AB = 8.4 in.
If you want to learn more about right triangles:
#SPJ1
