Question

in $\triangle abc$, if $a = 36$ cm and $mangle c = 23^circ$ , then what is the length of altitude $h$? round your answer to the nearest whole number.
(1 point)
$\bigcirc$ 39 cm
$\bigcirc$ 14 cm
$\bigcirc$ 33 cm
$\bigcirc$ 92 cm

Explanation:

Step1: Identify right triangle relation

The altitude $h$ forms a right triangle with side $a$, where $h$ is opposite $\angle C$. Use $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.
$\sin(23^\circ)=\frac{h}{a}$

Step2: Solve for $h$

Rearrange to isolate $h$, substitute $a=36$ cm.
$h = a\times\sin(23^\circ) = 36\times\sin(23^\circ)$

Step3: Calculate and round

Compute $\sin(23^\circ)\approx0.3907$, then find $h$ and round to whole number.
$h\approx36\times0.3907\approx14.065$

Answer:

B. 14 cm