A building casts a shadow reaching 13 feet from the base of the building, with a diagonal distance of 15 feet from the top of the building. Using the inverse of sine, what is the approximate angle formed between the top of the building and the shadow?(1 point)

Question

Responses

45°
45°

30°
30°

60°
60°

90°

Answer 1

To find the angle formed between the top of the building and the shadow, we can use the sine function.

We have:

• The opposite side (the height of the building, which we need to find using the Pythagorean theorem) and
• The hypotenuse (the diagonal distance from the top of the building to the end of the shadow, which is 15 feet).

From the information provided, we can calculate the height of the building using the Pythagorean theorem:

Let \( h \) be the height of the building. According to the Pythagorean theorem:

\[ h^2 + 13^2 = 15^2 \]

Calculating:

\[ h^2 + 169 = 225 \]

Subtracting 169 from both sides gives us:

\[ h^2 = 56 \]

Taking the square root:

\[ h = \sqrt{56} \approx 7.48 \text{ feet} \]

Now, we can calculate the angle \( \theta \) using the sine function:

\[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{h}{15} \approx \frac{7.48}{15} \]

Calculating the sine value:

\[ \sin(\theta) \approx 0.4987 \]

Now, using the inverse sine (arcsine) function:

\[ \theta \approx \arcsin(0.4987) \approx 30^\circ \]

Therefore, the approximate angle formed between the top of the building and the shadow is:

30°