Question

a 5 ft ladder leans on a wall from a horizontal level ground at an angle of 38°, as shown below. how high is the point at which the ladder touches the wall from the ground?
a
\\( \frac { 5 } { \cos 38 } \\)
b
\\( \frac { 5 } { \sin 38 } \\)
c
\\( \frac { \sin 38 } { 5 } \\)
d
5 cos 38
e
5 sin 38

Explanation:

Step1: Recall the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the ladder length is the hypotenuse (\(c = 5\) ft), the height on the wall is the side opposite to the given angle (\(\theta=38^{\circ}\)), let the height be \(h\).

Step2: Apply the sine formula

We have \(\sin(38^{\circ})=\frac{h}{5}\).

Step3: Solve for \(h\)

Multiply both sides by \(5\), so \(h = 5\sin(38^{\circ})\).

Answer:

E. \(5\sin38\)