Please help quick! Solve for the right triangle shown in the figure.

Question

asked Feb 17, 2020 221k views

2 Answers

Sachink · Answer 1 · 2020-02-23T10:37:17+0000

Answer: option c.

Explanation:

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:

$c=AB\\a=BC=7.50mi\\b=AC=11.43mi$

Substituting values and solving for AB, we get:

$AB^2=(7.50mi)^2+(11.43mi)^2\\\\AB=√((7.50mi)^2+(11.43mi)^2)\\\\AB=13.7mi$

To find ∠B you can use the Arctangent. Then, this is:

$\angle B=arctan((11.43mi)/(7.50m))=56.7\°$

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

$\angle A=180\°-56.7\°-90\°\\\\\angle A=33.3\°$