Right Triangle
ABC
has the following dimensions
AB =9
,
m∠A = 28°
and
m∠C = 90°
. Find the other measurements of the triangle,
AC
,
BC
and
m∠B
.
To find the measurement of AC, we can use the sine rule. The sine rule states that in any triangle, the ratio of the length of a side to the sine of the opposite angle is constant.
Using the sine rule, we have:
AC / sin(28°) = AB / sin(90°)
AC / sin(28°) = 9 / 1
AC = sin(28°) * 9
AC ≈ 4.28
To find the measurement of BC, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Using the Pythagorean theorem, we have:
BC^2 = AB^2 + AC^2
BC^2 = 9^2 + 4.28^2
BC^2 ≈ 81 + 18.30
BC^2 ≈ 99.30
BC ≈ √99.30
BC ≈ 9.96
To find the measurement of angle B, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
m∠B = 180° - m∠A - m∠C
m∠B = 180° - 28° - 90°
m∠B = 62°
So, the other measurements of the triangle are:
AC ≈ 4.28
BC ≈ 9.96
m∠B = 62°