Question

a triangle upper A upper B upper C
In △ABC
, if a=36 cm
and m∠C = 23°
, then what is the length of altitude h
? Round your answer to the nearest whole number.

(1 point)
Responses

39 cm
39 cm

14 cm
14 cm

33 cm
33 cm

92 cm

Answer 1

To find the length of the altitude \( h \) from vertex \( C \) to side \( a \) (which is opposite angle \( C \)) in triangle \( ABC \), we can use the formula:

\[
h = a \cdot \sin(C)
\]

where \( a = 36 \, \text{cm} \) and \( C = 23^\circ \).

First, we need to calculate \( \sin(23^\circ) \). Using a calculator, we find:

\[
\sin(23^\circ) \approx 0.3907
\]

Now, substituting the values into the formula:

\[
h = 36 \, \text{cm} \cdot \sin(23^\circ) \approx 36 \, \text{cm} \cdot 0.3907 \approx 14.1 \, \text{cm}
\]

Rounding to the nearest whole number, we find:

\[
h \approx 14 \, \text{cm}
\]

Thus, the length of the altitude \( h \) is **14 cm**.