Using tangent of an angle and the Pythagorean Theorem, AB is 8.4 inches and AC is 13.1 inches.
What is the tangent of an angle?
The tangent of an angle in a right-angle triangle is the ratio of the height and the base of that triangle.
If the tangent of an angle is represented as X, then tan X = (height/base).
What is the Pythagorean Theorem?
The Pythagorean Theorem states that, in a right-angle triangle, the square of the hypotenuse is equal to the sum of the squares of the base and the height.
Given, the length of the side BC of the given triangle ABC = 10 inches.
The ∠ACB of the triangle ABC = 40°.
We know, tan ∠ACB = height/base = AB/ BC = AB/10
⇒ tan 40° = AB/10
⇒ AB = 10 × tan 40° = 10 × 0.84 inches = 8.4 inches.
Now, AC = √[(AB)² + (BC)²]
= √[(8.4)² + (10)²] inches
= √(170.56) inches
= 13.1 inches
Learn more about the tangent of an angle: https://brainly.com/question/22221907
#SPJ2
