Which of the following triangles are right triangles?

Question

6. Which of the following triangles are right triangles? Check all that apply.
A triangle with side lengths 5, 12, 13
A triangle with side lengths 6 inches, 8 inches, 10 inches
A triangle with side lengths 8, 15, 17
A triangle with side lengths 4, 5, 6

7. The radian measure of an angle that is 105 ° 32' 45'' is _____.
.59 radians
1.84 radians
1.59 radians
2.78 radians

8. An angle measuring π/8 radians is equal to which of the angle measures given below? Check all that apply.
22 ° 5'
22 ° 30'
22.5 °
39.25 °

9. The arc corresponding to a central angle of 35° in a circle of radius 10 feet measures _____ feet. Round your answer to two decimal places.

10. If the arc length shown in blue is 21.3 inches, then θ to the nearest hundredth of a radian is _____.
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Answer 1

6. You can plug each set of numbers into the Pythagorean Theorem, or recognize that 5/12/13, 6/8/10 and 8/15/17 are each Pythagorean triples. 4/5/6 does not satisfy the Pythagorean Theorem, so that does not represent a right triangle.

 

7. You convert degree measure to radians by dividing degrees by 180 and multiplying by pi. But you first need to convert the minutes and seconds to decimal form.

 

105° 32' 45"=102 + 32/60 + 45/3600 = 105.5458°

 

So the conversion to radians becomes 102.5458 / 180 * pi=1.84 radians.

 

8. Converting from radians to degrees is the opposite process to what we just did. We divide by pi and multiply by 180. (pi/8) * (180/pi) = (180/8) = 22.5°. This can also be written as 22° 30'. 

 

9. The arc length can be calculated by multiplying the radian measure of the central angle by the radius. 

 

L=35 * (pi/180) * 10 =6.11 feet.

 

 

 

Your link in question #10 is broken. 

 

Jeff