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
92 cm
92 cm
14 cm
14 cm
39 cm
39 cm
33 cm
To find the length of altitude \( h \) in triangle \(\triangle ABC\), we can use the formula:
\[ h = a \cdot \sin(C) \]
Given that \( a = 36 \) cm and \( m\angle C = 23^\circ \), we can use these values to find the length of altitude \( h \) by plugging them into the formula:
\[ h = 36 \cdot \sin(23^\circ) \]
Using a calculator to find the sine of \(23^\circ\), we get:
\[ h = 36 \cdot 0.390731 \approx 14 \text{ cm} \]
Therefore, the length of altitude \( h \) is approximately 14 cm.
So, the correct answer is:
14 cm