Answer:
Unknown side = 28
tan B = 7/24
Explanation:
The question is incomplete. Here is the complete question.
Suppose ABC is a right triangle with sides of lengths a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the value of the indicated trigonometric function of the given angle. Rationalize the denominator if applicable. Find tan B when a = 96 and c = 100.
Pythagoras theorem states that the square of the hypotenuse side of a right angled triangle is equal to the sum of the square of its other two sides. Mathematically c² = a²+b² where c is the hypotenuse and a,b are the other two sides.
From the question, we are given a = 96 and c = 100, to get the unknown side 'b', we will substitute the given values into the formula above;
c² = a²+b²
100² = 96² +b²
b² = 100² - 96²
b² = 10,000 - 9216
b² = 784
b = √784
b = 28
Hence, the unknown length is 28.
To get tanB, we will use the SOH, CAH, TOA trigonometry identity
According to TOA, tan B = opposite/adjacent
tan B = b/a (note that side b is the opposite in this case since the angle we are considering is B)
Given b = 28 and a = 96
tan B = 28/96
tan B = 4*7/4*24
tan B = 7/24