Answer:
11 inches
Step-by-step explanation:
Applying the Pythagorean theorem, the length of b, to the nearest tenth, is: 11.2.
<h3>What is the Pythagorean Theorem?</h3>
The Pythagorean theorem is the theorem that is applied when finding any length of a right triangle. Where a and b are the smaller sides of the right triangle, and c is the longest side (hypotenuse) of the right triangle, the Pythagorean theorem states that: a² + b² = c².
We are given the following regarding a right triangle:
a = 10 (one of the smallest side)
c = 15 (the longest side/hypotenuse)
Plug in the values into a² + b² = c²:
10² + b² = 15²
100 + b² = 225
Subtract 100 from both sides
100 + b² - 100 = 225 - 100
b² = 125
Square both sides
√b² = √125
b ≈ 11.2
The length of b, to the nearest tenth, is: 11.2.
Learn more about the Pythagorean theorem on:
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if there's 3 counselors / 45 students.
3 counselors / 45 students = 1 counselor / 15 student
10 counselors multiplied by 15 students = 150 maximum students allowed.
Tanya paints 55 ft^2 / 30mins.
60 mins = 1 hour
60 mins / 30 mins = 2
55 multiplied by 2 = 110
(There were two different people mentioned in the problem)
Tanya, or Angela, paints 110 square feet every hour.
What are the theorems we can use?
Probably the most relevant is the angle at a point on the circle subtended by a chord has a measure equal to half the arc indicated by the chord.
By the theorem,
angle AEB = angle ADB = (1/2) arc AC = (1/2) 110 = 55 deg
angle BAE = angle DBE = (1/2) arc DE = (1/2) 130 = 65 deg
angle BKD + angle KDB + angle DBK = 180 deg
angle BKD + angle ADB + angle DBE = 180 deg
angle BKD = 180 - 55 - 65 = 60 degrees
Answer: 60 degrees