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

Question

asked Sep 11, 2020 17.5k views

1 Answer

Jorgeca · Answer 1 · 2020-09-18T04:38:48+0000

Answer: option c.

Explanation:

To find AB you can use this trigonometric identity:

$tan\alpha=(opposite)/(adjacent)$

In this case:

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

Substituting values and solving for AC, we get:

$tan(48.8\°)=(1.6in)/(AC)\\\\AC=(1.6in)/(tan(48.8\°))\\\\AC=1.4in$

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:

$AB^2=(1.6in)^2+(1.4in)^2\\\\AB=√((1.6in)^2+(1.4in)^2)\\\\AB=2.1in$

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

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