Question

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

Answer 1

Answer: option c.

Step-by-step explanation:

To find AB you can use this trigonometric identity:

$tan\alpha=\frac{opposite}{adjacent}$

 In this case:

$\alpha=\angle A=48.8\°\\opposite=BC=1.6in\\adjacent=AC$

Substituting values and solving for AC, we get:

$tan(48.8\°)=\frac{1.6in}{AC}\\\\AC=\frac{1.6in}{tan(48.8\°)}\\\\AC=1.4in$

To find AB you can use the Pythagorean Theorem:

$c^2=a^2+b^2$

Where "c" is the hypotenuse and "a" and "b" are the legs of the triangle.

In this case:

$c=AB\\b=AC=1.4in\\\\a=BC=1.6in$

Substituting values and solving for AB, we get:

 $AB^2=(1.6in)^2+(1.4in)^2\\\\AB=\sqrt{(1.6in)^2+(1.4in)^2}\\\\AB=2.1in$

 Since the sum of the interior angles of a triangle is 180 degrees, we know that  ∠B is:

  $\angle B=180\°-\angle A-\angle C\\\\\angle B=180\°-48.8\°-90\°\\\\\angle B=41.2\°$