Question

trig mixed practice
8 of 9
bob, the roofer, is standing on top of a 23 ft. two-story house. he sees his co-worker, wendy, at an angle of depression of 15 degrees. which equations can used to find the straight line distance, x, from the top of the house to wendy on the ground? choose all that are correct
$sin(15) = \frac{23}{x}$
$\tan(15) = \frac{x}{23}$
$sin(75) = \frac{x}{23}$
$cos(75) = \frac{23}{x}$
$cos(15) = \frac{23}{x}$

Explanation:

Step1: Define right triangle components

We form a right triangle where:

• Vertical side (opposite to 15° angle of depression) = $23$ ft
• Hypotenuse = $x$ (straight line distance)
• Angle of depression = $15^\circ$, so the angle inside the triangle at Wendy is also $15^\circ$ (alternate interior angles), and the angle at the top of the house is $75^\circ$.

Step2: Relate sides with sine (15°)

Sine of 15° equals opposite over hypotenuse:
$\sin(15^\circ) = \frac{23}{x}$

Step3: Relate sides with cosine (75°)

Cosine of 75° equals adjacent over hypotenuse (the adjacent side to 75° is the 23 ft vertical side):
$\cos(75^\circ) = \frac{23}{x}$

Answer:

$\sin(15) = \frac{23}{x}$
$\cos(75) = \frac{23}{x}$