If D = 15 cm and θ = 69°, what is the value of F in cm? ( F is the hypotenuse and D is the  side adjacent to θ)

To find the value of \( F \) (the hypotenuse), we can use the trigonometric function cosine, since we have the adjacent side \( D \) and the angle \( \theta \).

The cosine of an angle is defined as:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{D}{F}
\]

Given:

\[
D = 15 \, \text{cm}, \quad \theta = 69^\circ
\]

We can rearrange the equation to solve for \( F \):

\[
F = \frac{D}{\cos(\theta)}
\]

Now, plug in the values:

\[
F = \frac{15}{\cos(69^\circ)}
\]

Using a calculator to find \( \cos(69^\circ) \):

\[
\cos(69^\circ) \approx 0.3584
\]

So,

\[
F = \frac{15}{0.3584} \approx 41.85 \, \text{cm}
\]

Thus, the value of \( F \) is approximately **41.85 cm**.

Would you like to ask anything else or need further details? Here are some related questions you might be interested in:

1. How do you calculate the adjacent side given the hypotenuse and angle?
2. What is the sine function and how does it relate to the hypotenuse and opposite side?
3. How do you use the tangent function to find unknown sides in a triangle?
4. What are the key trigonometric identities and how are they used in problems like this?
5. How does the angle of elevation or depression affect the length of the sides in a right triangle?

**Tip:** When solving trigonometric problems, always ensure your calculator is set to the correct mode (degrees or radians) based on the angle given.

If D = 15 cm and θ = 69°, what is the value of F in cm? (F is the hypotenuse and D is the side adjacent to θ)

Learn how to calculate the hypotenuse (F) of a right triangle using the cosine function, with D = 15 cm and θ = 69°. This problem applies trigonometry concepts and uses the formula F = D / cos(θ). Ideal for students in Grades 9-10.

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