The figure below shows triangle wooden frame ABC. The side AD of the frame has rotted and needs to be replaced. What is the length of the wood that is needed to replace AD? 4.2
5.7
2.5
1.3

AD = 4.2 in

Step-by-step explanation:

We'll begin by calculating the length AB. This can be obtained as follow:

Angle C = 15 + 30 = 45°

Adjacent = BC = 10 in

Opposite = AB =?

The length AB can be obtained by using the tan ratio as illustrated below:

Tan C = Opposite / Adjacent

Tan 45 = AB / 10

1 = AB / 10

Cross multiply

AB = 1 × 10

AB = 10 in

Next, we shall determine the length BD. This can be obtained as follow:

Angle C = 30°

Adjacent = BC = 10 in

Opposite = BD =?

The length BD can be obtained by using the tan ratio as illustrated below:

Tan C = Opposite / Adjacent

Tan 30 = BD / 10

0.5774 = BD / 10

Cross multiply

BD = 0.5774 × 10

BD = 5.8 in

Finally, we shall determine length AD. This can be obtained as follow:

AB = 10 in

BD = 5.8 in

AD =?

AB = BD + AD

10 = 5.8 + AD

Collect like terms

10 – 5.8 = AD

4.2 = AD

AD = 4.2 in

i just took the test, the correct answer is .. 31.5 in.

there is no question content here, but you for the free points! : d