A gauge is used to check the diameter of a crankshaft journal. It is constructed to make measurements on the basis of a right triangle with a 60.0° angle (see figure in the link below). Distance AB in the illustration is 10.6 cm. Find radius BC of the journal.
www.webassign.net/ewenmath10/13-5-013-alt.gif
so angle A = 30
sin30 = BC/AB
BC = ABsin30 = 10.6(1/2) = ...
10.6(1/2) = 5.3
I got 5.3 wrong
SOMEONE HELP ME!
According to the diagram you supplied and the given data,
the answer of 5.3 cm is correct.
To find the radius BC of the journal, we can use trigonometric ratios.
In the given figure, we have a right triangle ABC, where angle C is 90° and angle B is 60°. We are given the distance AB as 10.6 cm.
Now, let's label the sides of the triangle:
- Side AB = 10.6 cm (given)
- Side BC = radius of the journal (to be found)
- Side AC = hypotenuse (we'll call it x)
Since we have a right triangle and angle B is 60°, we can use the trigonometric ratio of sine (sin). In this case, we need to use sine because we have the opposite and hypotenuse sides.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, we have:
sin(B) = AB / AC
Now, substituting the values we have:
sin(60°) = 10.6 cm / x
We know that sin(60°) is equal to √3/2, so we can rewrite the equation:
√3/2 = 10.6 cm / x
Next, we can cross-multiply to solve for x:
√3x = 10.6 cm * 2
√3x = 21.2 cm
To isolate x, we can square both sides of the equation:
(√3x)^2 = (21.2 cm)^2
3x = 449.44 cm^2
Finally, we can solve for x by dividing both sides of the equation by 3:
x = 449.44 cm^2 / 3
Therefore, the radius of BC, which is equal to x, is approximately 149.81 cm.