In
△ABC
, if
a=36 cm
and
m∠C=33°
, then what is the length of altitude
h
? Round your answer to the nearest whole number.
To find the length of the altitude h, we can use the trigonometric relationship in a right-angled triangle. In this case, we can use the sine function.
In triangle ABC, angle C is 33 degrees, which means that angle A is 90 - 33 = 57 degrees.
We can use the sine function to find the length of h:
sin(57 degrees) = h / a
To find h, we can rearrange the formula:
h = a * sin(57 degrees)
Substituting the given value a = 36 cm, we have:
h = 36 cm * sin(57 degrees)
Using a calculator, we find that sin(57 degrees) ≈ 0.8387.
So, h ≈ 36 cm * 0.8387 ≈ 30.194 cm.
Rounding to the nearest whole number, the length of altitude h is 30 cm.