find bd. write your answer as an integer or as a decimal rounded to the nearest tenth. bd =
find bd. write your answer as an integer or as a decimal rounded to the nearest tenth. bd =
Answer
Explanation:
Step1: Identify trig - ratio
In right - triangle $BCD$, we know the side adjacent to the given angle $\angle D = 63^{\circ}$ is $CD$ and we want to find the hypotenuse $BD$. We use the cosine function. The cosine of an angle in a right - triangle is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $\cos D=\frac{CD}{BD}$.
Step2: Rearrange the formula
We can rewrite the formula $\cos D=\frac{CD}{BD}$ to solve for $BD$. So, $BD = \frac{CD}{\cos D}$.
Step3: Substitute values
We are given that $CD = 4$ and $D = 63^{\circ}$. We know that $\cos63^{\circ}\approx0.454$. Substituting these values into the formula $BD=\frac{4}{\cos63^{\circ}}$, we get $BD=\frac{4}{0.454}\approx8.8$.
Answer:
$8.8$