Answer:
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
