What is the value of y? 11.6 ft 12.5 ft 16.5 ft 17.5 ft

2 answers
Question:

What is the value of y? 11.6 ft 12.5 ft 16.5 ft 17.5 ft

Answers

To solve the exercise shown in the picture attached, you must apply the following proccedure:

 1. First, you must apply the Pythagorean Theorem to calculate the heigth of the triangle, as below:

 a^2=b^2+c^2
 b=√(a^2-c^2)
 b=√(14)^2-(8)^2
 b=√132
 b=11.48

 2. Now, you must calculate the angle ∠BC, as below:

 Sin(α)^-1=opposite/hypotenuse
 Sin(BC)^-1=8/14
 ∠BC=34.84°

 3. Therefore, the angle ∠BA is:
 ∠BA=90°-34.84°
 ∠BA=55.15°

 4. Then, you have:

 Tan(55.15°)=y/11.48
 y=16.48

We know that

in the triangle BCD
 cos C=8/14
C=arc cos (8/14)> C=55.15°

sin C=BD/14> BD=14*sin 55.15> BD=11.49 ft

in the triangle ABC
180=∡A+∡B+∡C
∡A=180-(90+55.15)> ∡A=34.85°

tan A=BD/y> y=BD/tan A> y=11.49/tan 34.85> y=16.50 ft

the answer is
y=16.50 ft

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