right triangle ABC
B is vertex with right angle
<A=30
<C=60
AB= square root of 3 (cm)
what is BC and AC
AC 2
BC 1
To find the lengths of BC and AC in a right triangle, we can use trigonometric ratios. In this case, since we're given the measures of angles and one side length, we can use the sine and cosine ratios.
Let's start with BC. In a right triangle, the side opposite the right angle is called the hypotenuse. In this case, AB is the hypotenuse, and BC is the side adjacent to angle B.
The cosine ratio is defined as the adjacent side divided by the hypotenuse. So, we can use the cosine of angle B to find BC. The cosine of angle B is equal to BC divided by AB:
cos(B) = BC / AB
Since we know the value of AB is √3 cm, we can substitute it into the equation:
cos(B) = BC / √3
Next, we can use the given angle <A=30 degrees to determine the value of cos(B). The cosine of a complementary angle is equal to the sine of the angle. So, we have:
cos(B) = sin(90 - A) = sin(90 - 30) = sin(60) = √3 / 2
Substituting this value into the equation, we have:
√3 / 2 = BC / √3
To solve for BC, we can cross multiply:
BC = (√3 / 2) * √3
BC = √3 / 2 * √3
BC = (√3 * √3) / 2
BC = (√9) / 2
BC = 3 / 2
BC = 1.5 cm
So, BC is 1.5 cm.
To find AC, we can apply similar steps. AC is the side opposite angle C, which means it is the hypotenuse in this case. The sine ratio is defined as the opposite side divided by the hypotenuse. So, we can use the sine of angle C to find AC:
sin(C) = AC / AB
Since we know AB is √3 cm, we can substitute it into the equation:
sin(C) = AC / √3
Next, we can use the given angle <C=60 degrees to determine the value of sin(C):
sin(C) = sin(60) = √3 / 2
Substituting this value into the equation, we have:
√3 / 2 = AC / √3
To solve for AC, we can cross multiply:
AC = (√3 / 2) * √3
AC = √3 / 2 * √3
AC = (√3 * √3) / 2
AC = (√9) / 2
AC = 3 / 2
AC = 1.5 cm
So, AC is also 1.5 cm.