Question

for the triangle shown, find the length ad. (assume u = 11, v = 11, ∠x = 25°, and ∠y = 25°. round your answer to two decimal places.) ad =

Explanation:

Step1: Find angle $\angle BCA$

In $\triangle ABC$, the sum of interior angles of a triangle is $180^{\circ}$. Since $\angle B = \angle x=25^{\circ}$ and $\angle ACD=\angle y = 25^{\circ}$, then $\angle BCA=180^{\circ}- 25^{\circ}-25^{\circ}=130^{\circ}$.

Step2: Use the Law of Sines in $\triangle BCD$

In $\triangle BCD$, by the Law of Sines, $\frac{u}{\sin x}=\frac{BD}{\sin y}$. Substituting $u = 11$, $x = 25^{\circ}$, and $y = 25^{\circ}$, we get $\frac{11}{\sin25^{\circ}}=\frac{BD}{\sin25^{\circ}}$, so $BD = 11$.

Step3: Calculate $AD$

We know that $BA=v = 11$, and $AD=BA - BD$. Since $BA = 11$ and $BD = 11$, then $AD=11 - 11=0$.

Answer:

$0.00$