Question

PLEASE HELP! THANKS! AB=85m. Find the length of CD⎯⎯⎯⎯.

A. 5.3
B. 5.9
C. 6.7
D. 4.5

Answer 1

The length of CD is:

Option: B 5.9 m

Explanation:

We need to use the trigonometric ratio in order to find the value of the length of CD.

In right angled triangle CBA we have:

`\tan 28\°=(CB)/(AB)\\\\i.e.\\\\0.53171=(CB)/(85)\\\\i.e.\\\\CB=45.195`

Also, in right angled triangle i.e. ΔABD we have:

`\tan 31\°=(BD)/(AB)\\\\i.e.\\\\\tan 31\°=(CB+CD)/(85)\\\\i.e.\\\\CB+CD=\tan 31\°* 85\\\\i.e.\\\\CB+CD=51.0732\\\\i.e.\\\\CD=51.0732-CB\\\\i.e.\\\\CD=51.0732-45.195\\\\i.e.\\\\CD=5.8782`

which to the nearest tenth is:

`CD=5.9\ m`

Hence, option: B is the correct answer.

Answer 2

Option B. 5.9 m

Explanation:

step 1

Find the length of BC

we know that

tan(28°)=BC/AB

BC=(AB)tan(28°)

substitute values

BC=(85)tan(28°)=45.2 m

step 2

Find the length of BD

we know that

tan(31°)=BD/AB

BD=(AB)tan(31°)

substitute values

BD=(85)tan(31°)=51.1 m

step 3

Find the length of CD

we know that

CD=BD-BC

CD=51.1-45.2=5.9 m