Question

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

(10 points)
Responses

14 cm
14 cm

33 cm
33 cm

39 cm
39 cm

92 cm

Answer 1

To find the length of the altitude \( h \) from vertex \( C \) to side \( AB \) in triangle \( ABC \), we can use the formula for the area of a triangle. First, we will calculate the altitude using the formula:

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

where \( a \) is the length of side opposite angle \( C \) and \( C \) is the angle \( m\angle C \).

Given:
- \( a = 36 \, \text{cm} \)
- \( m\angle C = 23^\circ \)

Let's calculate \( h \):

\[
h = 36 \, \text{cm} \times \sin(23^\circ)
\]

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

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

Now plugging this value into the equation for \( h \):

\[
h \approx 36 \times 0.3907 \approx 14.06 \, \text{cm}
\]

Rounding this to the nearest whole number, we find:

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

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