Q:

Please help soon. Solve the right triangle shown in the figure.

Accepted Solution

A:
Answer: option c.Step-by-step explanation: To find AB you can use this trigonometric identity: [tex]tan\alpha=\frac{opposite}{adjacent}[/tex]  In this case: [tex]\alpha=\angle A=48.8\°\\opposite=BC=1.6in\\adjacent=AC[/tex] Substituting values and solving for AC, we get: [tex]tan(48.8\°)=\frac{1.6in}{AC}\\\\AC=\frac{1.6in}{tan(48.8\°)}\\\\AC=1.4in[/tex] To find AB you can use the Pythagorean Theorem: [tex]c^2=a^2+b^2[/tex] Where "c" is the hypotenuse and "a" and "b" are the legs of the triangle. In this case: [tex]c=AB\\b=AC=1.4in\\\\a=BC=1.6in[/tex] Substituting values and solving for AB, we get:  [tex]AB^2=(1.6in)^2+(1.4in)^2\\\\AB=\sqrt{(1.6in)^2+(1.4in)^2}\\\\AB=2.1in[/tex]  Since the sum of the interior angles of a triangle is 180 degrees, we know that  ∠B is:   [tex]\angle B=180\°-\angle A-\angle C\\\\\angle B=180\°-48.8\°-90\°\\\\\angle B=41.2\°[/tex]