Question

What is the value of y?



11.6 ft
12.5 ft
16.5 ft
17.5 ft

Answer 1

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

Answer 2

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