Use the figure below to find the exact value of the given trigonometric expression. 10
24
(figure not necessarily to scale)

A)
B)
C)
D)

Question

​Use the figure below to find the exact value of the given trigonometric expression.  ​ ​  10
24
(figure not necessarily to scale)
​
A)​ 
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

We can see that $ABCD$ is a rectangle with $AB=24$ and $BC=10$. Therefore, $\cos(\angle DAB) = \cos(90^\circ) = 0$. Using the cosine function in right triangle $ABD$, we have:
$$\cos(\angle ABD) = \frac{10}{\sqrt{10^2+24^2}}=\frac {5}{\sqrt{29^2}}=\frac{5}{29}$$
Using the double-angle identity for cosine, we have:
$$\cos(2\angle ABD) = 1-2\sin^2(\angle ABD)=1-2\left(\frac{24}{29}ight)^2=\frac{189}{841}$$
Therefore, the answer is $\boxed{	extbf{(D) } 11eacce6_1e50_6185_9f49_9b2d6a578142_TB7896_11}$

​Use the Figure Below to Find the Exact Value of the Given

Use the Figure Below to Find the Exact Value of the Given