Question

Find the unknown side length. Then find tan A. Write each answer as a fraction in simplest form and as a decimal. Round to four decimal places, if necessary.

Given:
Side B = 12
Side A = 60
Find tan(A).

Answer 1

To find the unknown side length, use the Pythagorean theorem. The unknown side is approximately 58.79. To find tan A, use the tangent function. tan A is approximately 1.021.

Step-by-step explanation:

To find the unknown side length, we can use the Pythagorean theorem. In a right triangle, the Pythagorean theorem states that the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, side B is the hypotenuse of the triangle. So, we have:

B^2 = A^2 + side^2

Substituting the given values:

12^2 = 60^2 + side^2

Simplifying:

144 = 3600 + side^2

Subtracting 3600 from both sides:

side^2 = 3600 - 144 = 3456

Taking the square root of both sides:

side = √3456 ≈ 58.79

Now, to find tan A, we can use the tangent function, which is the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is A and the adjacent side is side:

tan A = A / side

Substituting the given values:

tan A = 60 / 58.79 ≈ 1.021